diff --git a/Project.toml b/Project.toml
index c6331f956dd7..d3577f98ead8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -37,7 +37,7 @@ JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
 Nemo = "0.42.1"
 Pkg = "1.6"
-Polymake = "0.11.13"
+Polymake = "0.11.14"
 Preferences = "1"
 Random = "1.6"
 RandomExtensions = "0.4.3"
diff --git a/data/JohnsonMatrices/j10.mat b/data/JohnsonMatrices/j10.mat
deleted file mode 100644
index 51584e6e0747..000000000000
--- a/data/JohnsonMatrices/j10.mat
+++ /dev/null
@@ -1 +0,0 @@
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\ No newline at end of file
diff --git a/data/JohnsonMatrices/j13.mat b/data/JohnsonMatrices/j13.mat
deleted file mode 100644
index 01d438bea923..000000000000
--- a/data/JohnsonMatrices/j13.mat
+++ /dev/null
@@ -1 +0,0 @@
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\ No newline at end of file
diff --git a/data/JohnsonMatrices/j16.mat b/data/JohnsonMatrices/j16.mat
deleted file mode 100644
index 13a4ceb6c9cd..000000000000
--- a/data/JohnsonMatrices/j16.mat
+++ /dev/null
@@ -1 +0,0 @@
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\ No newline at end of file
diff --git a/data/JohnsonMatrices/j17.mat b/data/JohnsonMatrices/j17.mat
deleted file mode 100644
index b3ae6e594355..000000000000
--- a/data/JohnsonMatrices/j17.mat
+++ /dev/null
@@ -1 +0,0 @@
-{"_ns":{"Oscar":["https://github.com/oscar-system/Oscar.jl","0.15.0-DEV-a452c9dd24612f51f8bc2ab633ae0d2cce48f1bb"]},"_type":{"name":"MatElem","params":"a8145c6e-4ce2-483f-a2d1-410b95884449"},"data":[[[],[],[["1","1//4"],["2","1//4"]]],[[],[],[["1","-1//4"],["2","-1//4"]]],[[["0","1//2"]],[["0","1//2"]],[["1","1//4"]]],[[["0","1//2"]],[["0","-1//2"]],[["1","1//4"]]],[[["0","-1//2"]],[["0","1//2"]],[["1","1//4"]]],[[["0","-1//2"]],[["0","-1//2"]],[["1","1//4"]]],[[],[["2","1//4"]],[["1","-1//4"]]],[[],[["2","-1//4"]],[["1","-1//4"]]],[[["2","1//4"]],[],[["1","-1//4"]]],[[["2","-1//4"]],[],[["1","-1//4"]]]],"_refs":{"a8145c6e-4ce2-483f-a2d1-410b95884449":{"_type":"MatSpace","data":{"base_ring":"31437de7-39eb-4db8-9522-e69d64cae29b","ncols":"3","nrows":"10"}},"31437de7-39eb-4db8-9522-e69d64cae29b":{"_type":"EmbeddedNumField","data":{"num_field":"168b26a0-4f40-4bdf-b0dc-dda862c0cd9c","embedding":"4956a855-3458-4f98-85c1-e0a7f0487ba2"}},"168b26a0-4f40-4bdf-b0dc-dda862c0cd9c":{"_type":"AbsSimpleNumField","data":{"def_pol":{"_type":{"name":"PolyRingElem","params":"41d0500b-5855-45ef-9508-e5aace4fe9b8"},"data":[["0","-8"],["4","1"]]},"var":"a"}},"4956a855-3458-4f98-85c1-e0a7f0487ba2":{"_type":"Hecke.AbsSimpleNumFieldEmbedding","data":{"num_field":"168b26a0-4f40-4bdf-b0dc-dda862c0cd9c","data":{"_type":{"name":"AcbFieldElem","params":{"_type":"AcbField","data":"34"}},"data":["35d13f32b -21 20000003 -3f","0 0 0 0"]}}},"41d0500b-5855-45ef-9508-e5aace4fe9b8":{"_type":"PolyRing","data":{"base_ring":{"_type":"QQField"},"symbols":["x"]}}}}
\ No newline at end of file
diff --git a/data/JohnsonMatrices/j18.mat b/data/JohnsonMatrices/j18.mat
deleted file mode 100644
index ab24ec8b2bf5..000000000000
--- a/data/JohnsonMatrices/j18.mat
+++ /dev/null
@@ -1 +0,0 @@
-{"_ns":{"Oscar":["https://github.com/oscar-system/Oscar.jl","0.15.0-DEV-a452c9dd24612f51f8bc2ab633ae0d2cce48f1bb"]},"_type":{"name":"MatElem","params":"988ac1b9-5cd0-4665-9dce-15da57fc9a79"},"data":[[[[["0","0"],"1//2"]],[[["0","1"],"1//2"]],[[["0","0"],"1//2"]]],[[[["0","0"],"1//2"]],[[["0","1"],"1//2"]],[[["0","0"],"-1//2"]]],[[[["0","0"],"1//2"]],[[["0","1"],"-1//2"]],[[["0","0"],"1//2"]]],[[[["0","0"],"1//2"]],[[["0","1"],"-1//2"]],[[["0","0"],"-1//2"]]],[[[["0","0"],"-1//2"]],[[["0","1"],"1//2"]],[[["0","0"],"1//2"]]],[[[["0","0"],"-1//2"]],[[["0","1"],"1//2"]],[[["0","0"],"-1//2"]]],[[[["0","0"],"-1//2"]],[[["0","1"],"-1//2"]],[[["0","0"],"1//2"]]],[[[["0","0"],"-1//2"]],[[["0","1"],"-1//2"]],[[["0","0"],"-1//2"]]],[[[["0","0"],"1"]],[],[[["0","0"],"1//2"]]],[[[["0","0"],"1"]],[],[[["0","0"],"-1//2"]]],[[[["0","0"],"-1"]],[],[[["0","0"],"1//2"]]],[[[["0","0"],"-1"]],[],[[["0","0"],"-1//2"]]],[[[["0","0"],"1//2"]],[[["0","1"],"-1//6"]],[[["1","1"],"1//3"],[["0","0"],"1//2"]]],[[[["0","0"],"-1//2"]],[[["0","1"],"-1//6"]],[[["1","1"],"1//3"],[["0","0"],"1//2"]]],[[],[[["0","1"],"1//3"]],[[["1","1"],"1//3"],[["0","0"],"1//2"]]]],"_refs":{"988ac1b9-5cd0-4665-9dce-15da57fc9a79":{"_type":"MatSpace","data":{"base_ring":"30c27ba1-0163-4bbd-b5c1-c97594455965","ncols":"3","nrows":"15"}},"30c27ba1-0163-4bbd-b5c1-c97594455965":{"_type":"EmbeddedNumField","data":{"num_field":"9af848a4-4f23-41f2-a6df-3b7034350a7c","embedding":"bed344fa-79a1-42b7-8b66-1cfede60ab1f"}},"9af848a4-4f23-41f2-a6df-3b7034350a7c":{"_type":"AbsNonSimpleNumField","data":{"def_pols":{"_type":{"name":"Vector","params":{"name":"PolyRingElem","params":"41d0500b-5855-45ef-9508-e5aace4fe9b8"}},"data":[[["0","-2"],["2","1"]],[["0","-3"],["2","1"]]]},"vars":["sqrt(2)","sqrt(3)"]}},"bed344fa-79a1-42b7-8b66-1cfede60ab1f":{"_type":"Hecke.AbsNonSimpleNumFieldEmbedding","data":{"num_field":"9af848a4-4f23-41f2-a6df-3b7034350a7c","data":{"_type":{"name":"Tuple","params":[{"name":"AcbFieldElem","params":{"_type":"AcbField","data":"64"}},{"name":"AcbFieldElem","params":{"_type":"AcbField","data":"64"}}]},"data":[["2d413cccfe779921 -3d 16a09e69 -5b","0 0 0 0"],["ddb3d742c265539d -3f 1279a749 -5a","0 0 0 0"]]}}},"41d0500b-5855-45ef-9508-e5aace4fe9b8":{"_type":"PolyRing","data":{"base_ring":{"_type":"QQField"},"symbols":["x"]}}}}
\ No newline at end of file
diff --git a/data/JohnsonMatrices/j20.mat b/data/JohnsonMatrices/j20.mat
deleted file mode 100644
index fbeafdd7bea6..000000000000
--- a/data/JohnsonMatrices/j20.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j21.mat b/data/JohnsonMatrices/j21.mat
deleted file mode 100644
index 0eb63eb52a56..000000000000
--- a/data/JohnsonMatrices/j21.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j22.mat b/data/JohnsonMatrices/j22.mat
deleted file mode 100644
index 8a19322b1ea3..000000000000
--- a/data/JohnsonMatrices/j22.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j23.mat b/data/JohnsonMatrices/j23.mat
deleted file mode 100644
index 060c51559890..000000000000
--- a/data/JohnsonMatrices/j23.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j24.mat b/data/JohnsonMatrices/j24.mat
deleted file mode 100644
index 6af940960675..000000000000
--- a/data/JohnsonMatrices/j24.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j25.mat b/data/JohnsonMatrices/j25.mat
deleted file mode 100644
index 6234d274cdb7..000000000000
--- a/data/JohnsonMatrices/j25.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j30.mat b/data/JohnsonMatrices/j30.mat
deleted file mode 100644
index 5c7a04f2bf4c..000000000000
--- a/data/JohnsonMatrices/j30.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j32.mat b/data/JohnsonMatrices/j32.mat
deleted file mode 100644
index b0b63eac5884..000000000000
--- a/data/JohnsonMatrices/j32.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j33.mat b/data/JohnsonMatrices/j33.mat
deleted file mode 100644
index 7b6a56c0f2f3..000000000000
--- a/data/JohnsonMatrices/j33.mat
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diff --git a/data/JohnsonMatrices/j34.mat b/data/JohnsonMatrices/j34.mat
deleted file mode 100644
index f4b50597c62a..000000000000
--- a/data/JohnsonMatrices/j34.mat
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diff --git a/data/JohnsonMatrices/j35.mat b/data/JohnsonMatrices/j35.mat
deleted file mode 100644
index e033425725ad..000000000000
--- a/data/JohnsonMatrices/j35.mat
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diff --git a/data/JohnsonMatrices/j36.mat b/data/JohnsonMatrices/j36.mat
deleted file mode 100644
index eb5952b497bf..000000000000
--- a/data/JohnsonMatrices/j36.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j38.mat b/data/JohnsonMatrices/j38.mat
deleted file mode 100644
index 79440bb1971f..000000000000
--- a/data/JohnsonMatrices/j38.mat
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diff --git a/data/JohnsonMatrices/j39.mat b/data/JohnsonMatrices/j39.mat
deleted file mode 100644
index 6de8d423ac2a..000000000000
--- a/data/JohnsonMatrices/j39.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j40.mat b/data/JohnsonMatrices/j40.mat
deleted file mode 100644
index d10900d8caaa..000000000000
--- a/data/JohnsonMatrices/j40.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j41.mat b/data/JohnsonMatrices/j41.mat
deleted file mode 100644
index 151c92e82e4d..000000000000
--- a/data/JohnsonMatrices/j41.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j42.mat b/data/JohnsonMatrices/j42.mat
deleted file mode 100644
index 65013ffe7d67..000000000000
--- a/data/JohnsonMatrices/j42.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j43.mat b/data/JohnsonMatrices/j43.mat
deleted file mode 100644
index eb4add817090..000000000000
--- a/data/JohnsonMatrices/j43.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j44.mat b/data/JohnsonMatrices/j44.mat
deleted file mode 100644
index b332c5fbcbc2..000000000000
--- a/data/JohnsonMatrices/j44.mat
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diff --git a/data/JohnsonMatrices/j45.mat b/data/JohnsonMatrices/j45.mat
deleted file mode 100644
index 91e9493b1ce4..000000000000
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diff --git a/data/JohnsonMatrices/j46.mat b/data/JohnsonMatrices/j46.mat
deleted file mode 100644
index f6fb330851d3..000000000000
--- a/data/JohnsonMatrices/j46.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j47.mat b/data/JohnsonMatrices/j47.mat
deleted file mode 100644
index df6c93da63b2..000000000000
--- a/data/JohnsonMatrices/j47.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j48.mat b/data/JohnsonMatrices/j48.mat
deleted file mode 100644
index 31f239118af0..000000000000
--- a/data/JohnsonMatrices/j48.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j49.mat b/data/JohnsonMatrices/j49.mat
deleted file mode 100644
index 606467e2253e..000000000000
--- a/data/JohnsonMatrices/j49.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j50.mat b/data/JohnsonMatrices/j50.mat
deleted file mode 100644
index e5fb70925d5b..000000000000
--- a/data/JohnsonMatrices/j50.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j51.mat b/data/JohnsonMatrices/j51.mat
deleted file mode 100644
index 6c03ff3210fa..000000000000
--- a/data/JohnsonMatrices/j51.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j52.mat b/data/JohnsonMatrices/j52.mat
deleted file mode 100644
index 021fa3f5c808..000000000000
--- a/data/JohnsonMatrices/j52.mat
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diff --git a/data/JohnsonMatrices/j53.mat b/data/JohnsonMatrices/j53.mat
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index e472333dea6c..000000000000
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diff --git a/data/JohnsonMatrices/j54.mat b/data/JohnsonMatrices/j54.mat
deleted file mode 100644
index 5a1167af96be..000000000000
--- a/data/JohnsonMatrices/j54.mat
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diff --git a/data/JohnsonMatrices/j55.mat b/data/JohnsonMatrices/j55.mat
deleted file mode 100644
index f33adbfff95a..000000000000
--- a/data/JohnsonMatrices/j55.mat
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diff --git a/data/JohnsonMatrices/j56.mat b/data/JohnsonMatrices/j56.mat
deleted file mode 100644
index 67fbf797c717..000000000000
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diff --git a/data/JohnsonMatrices/j57.mat b/data/JohnsonMatrices/j57.mat
deleted file mode 100644
index 60440082d3bc..000000000000
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diff --git a/data/JohnsonMatrices/j58.mat b/data/JohnsonMatrices/j58.mat
deleted file mode 100644
index 3146e5b2c804..000000000000
--- a/data/JohnsonMatrices/j58.mat
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diff --git a/data/JohnsonMatrices/j59.mat b/data/JohnsonMatrices/j59.mat
deleted file mode 100644
index 0915d6388755..000000000000
--- a/data/JohnsonMatrices/j59.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j60.mat b/data/JohnsonMatrices/j60.mat
deleted file mode 100644
index 1f879ef9ba24..000000000000
--- a/data/JohnsonMatrices/j60.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j61.mat b/data/JohnsonMatrices/j61.mat
deleted file mode 100644
index 29f6e6b380f9..000000000000
--- a/data/JohnsonMatrices/j61.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j64.mat b/data/JohnsonMatrices/j64.mat
deleted file mode 100644
index 478346654c3b..000000000000
--- a/data/JohnsonMatrices/j64.mat
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index 803424dd31af..000000000000
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diff --git a/data/JohnsonMatrices/j69.mat b/data/JohnsonMatrices/j69.mat
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index bde808fec649..000000000000
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diff --git a/data/JohnsonMatrices/j70.mat b/data/JohnsonMatrices/j70.mat
deleted file mode 100644
index 2517ba0484dc..000000000000
--- a/data/JohnsonMatrices/j70.mat
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diff --git a/data/JohnsonMatrices/j71.mat b/data/JohnsonMatrices/j71.mat
deleted file mode 100644
index 77bc63f180ca..000000000000
--- a/data/JohnsonMatrices/j71.mat
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@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j72.mat b/data/JohnsonMatrices/j72.mat
deleted file mode 100644
index 145ee2790d46..000000000000
--- a/data/JohnsonMatrices/j72.mat
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diff --git a/data/JohnsonMatrices/j73.mat b/data/JohnsonMatrices/j73.mat
deleted file mode 100644
index eca2f7bcd294..000000000000
--- a/data/JohnsonMatrices/j73.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j74.mat b/data/JohnsonMatrices/j74.mat
deleted file mode 100644
index f1ffbb2a9717..000000000000
--- a/data/JohnsonMatrices/j74.mat
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diff --git a/data/JohnsonMatrices/j75.mat b/data/JohnsonMatrices/j75.mat
deleted file mode 100644
index 9271d09a8ac8..000000000000
--- a/data/JohnsonMatrices/j75.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j77.mat b/data/JohnsonMatrices/j77.mat
deleted file mode 100644
index 9987700dca6b..000000000000
--- a/data/JohnsonMatrices/j77.mat
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diff --git a/data/JohnsonMatrices/j78.mat b/data/JohnsonMatrices/j78.mat
deleted file mode 100644
index 1ba19949edbf..000000000000
--- a/data/JohnsonMatrices/j78.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j79.mat b/data/JohnsonMatrices/j79.mat
deleted file mode 100644
index 75931915a512..000000000000
--- a/data/JohnsonMatrices/j79.mat
+++ /dev/null
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diff --git a/data/JohnsonMatrices/j82.mat b/data/JohnsonMatrices/j82.mat
deleted file mode 100644
index 54eef5960be3..000000000000
--- a/data/JohnsonMatrices/j82.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j84.mat b/data/JohnsonMatrices/j84.mat
deleted file mode 100644
index 803f3d1c9551..000000000000
--- a/data/JohnsonMatrices/j84.mat
+++ /dev/null
@@ -1 +0,0 @@
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diff --git a/data/JohnsonMatrices/j85.mat b/data/JohnsonMatrices/j85.mat
deleted file mode 100644
index f75a5747596a..000000000000
--- a/data/JohnsonMatrices/j85.mat
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diff --git a/data/JohnsonMatrices/j86.mat b/data/JohnsonMatrices/j86.mat
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index a1a67ba0f12b..000000000000
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diff --git a/data/JohnsonMatrices/j87.mat b/data/JohnsonMatrices/j87.mat
deleted file mode 100644
index d18cae32c940..000000000000
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diff --git a/data/JohnsonMatrices/j88.mat b/data/JohnsonMatrices/j88.mat
deleted file mode 100644
index 231bc362d43e..000000000000
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diff --git a/data/JohnsonMatrices/j89.mat b/data/JohnsonMatrices/j89.mat
deleted file mode 100644
index 834c8ddbc3c4..000000000000
--- a/data/JohnsonMatrices/j89.mat
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diff --git a/data/JohnsonMatrices/j9.mat b/data/JohnsonMatrices/j9.mat
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index 8732e628b2fc..000000000000
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diff --git a/data/JohnsonMatrices/j90.mat b/data/JohnsonMatrices/j90.mat
deleted file mode 100644
index 80cde9c68e98..000000000000
--- a/data/JohnsonMatrices/j90.mat
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diff --git a/data/JohnsonSolids/j10.mrdi b/data/JohnsonSolids/j10.mrdi
new file mode 100644
index 000000000000..e881c0c3fef7
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diff --git a/data/JohnsonSolids/j16.mrdi b/data/JohnsonSolids/j16.mrdi
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diff --git a/data/JohnsonSolids/j18.mrdi b/data/JohnsonSolids/j18.mrdi
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diff --git a/data/JohnsonSolids/j20.mrdi b/data/JohnsonSolids/j20.mrdi
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diff --git a/data/JohnsonSolids/j21.mrdi b/data/JohnsonSolids/j21.mrdi
new file mode 100644
index 000000000000..3b98157cb9e2
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diff --git a/data/JohnsonSolids/j22.mrdi b/data/JohnsonSolids/j22.mrdi
new file mode 100644
index 000000000000..23a000b97e0d
--- /dev/null
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diff --git a/data/JohnsonSolids/j30.mrdi b/data/JohnsonSolids/j30.mrdi
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diff --git a/data/JohnsonSolids/j32.mrdi b/data/JohnsonSolids/j32.mrdi
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diff --git a/data/JohnsonSolids/j33.mrdi b/data/JohnsonSolids/j33.mrdi
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diff --git a/data/JohnsonSolids/j34.mrdi b/data/JohnsonSolids/j34.mrdi
new file mode 100644
index 000000000000..b744c91899f4
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diff --git a/data/JohnsonSolids/j39.mrdi b/data/JohnsonSolids/j39.mrdi
new file mode 100644
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diff --git a/data/JohnsonSolids/j40.mrdi b/data/JohnsonSolids/j40.mrdi
new file mode 100644
index 000000000000..c1cfec46e6f6
--- /dev/null
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diff --git a/data/JohnsonSolids/j41.mrdi b/data/JohnsonSolids/j41.mrdi
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diff --git a/data/JohnsonSolids/j42.mrdi b/data/JohnsonSolids/j42.mrdi
new file mode 100644
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diff --git a/data/JohnsonSolids/j43.mrdi b/data/JohnsonSolids/j43.mrdi
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diff --git a/data/JohnsonSolids/j44.mrdi b/data/JohnsonSolids/j44.mrdi
new file mode 100644
index 000000000000..51600c1e92a4
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diff --git a/data/JohnsonSolids/j46.mrdi b/data/JohnsonSolids/j46.mrdi
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diff --git a/data/JohnsonSolids/j61.mrdi b/data/JohnsonSolids/j61.mrdi
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diff --git a/data/JohnsonSolids/j73.mrdi b/data/JohnsonSolids/j73.mrdi
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diff --git a/data/JohnsonSolids/j75.mrdi b/data/JohnsonSolids/j75.mrdi
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diff --git a/data/JohnsonSolids/j77.mrdi b/data/JohnsonSolids/j77.mrdi
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diff --git a/data/JohnsonSolids/j78.mrdi b/data/JohnsonSolids/j78.mrdi
new file mode 100644
index 000000000000..914c44948e4e
--- /dev/null
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diff --git a/data/JohnsonSolids/j82.mrdi b/data/JohnsonSolids/j82.mrdi
new file mode 100644
index 000000000000..6f1688914d24
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diff --git a/data/JohnsonSolids/j84.mrdi b/data/JohnsonSolids/j84.mrdi
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diff --git a/data/JohnsonSolids/j86.mrdi b/data/JohnsonSolids/j86.mrdi
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diff --git a/data/JohnsonSolids/j88.mrdi b/data/JohnsonSolids/j88.mrdi
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diff --git a/data/JohnsonSolids/j89.mrdi b/data/JohnsonSolids/j89.mrdi
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diff --git a/data/JohnsonSolids/j90.mrdi b/data/JohnsonSolids/j90.mrdi
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diff --git a/data/JohnsonSolids/j92.mrdi b/data/JohnsonSolids/j92.mrdi
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\ No newline at end of file
diff --git a/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl b/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl
index 6eaff26ae551..59b269779f78 100644
--- a/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl
+++ b/src/AlgebraicGeometry/Surfaces/SurfacesP4.jl
@@ -48,7 +48,7 @@ export rational_d11_pi11_ss_inf
 export veronese
 
 function surface(n::String)
-  n = joinpath(oscardir, "data", "Surfaces", n)
+  n = joinpath(oscardir, "data", "Surfaces", "$n" * ".mrdi")
   I = load(n)
   S = base_ring(I)
   R = grade(S)[1]
diff --git a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
index 4c221c75bc5d..aca35c61ff0c 100644
--- a/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
+++ b/src/PolyhedralGeometry/Polyhedron/standard_constructions.jl
@@ -318,9 +318,9 @@ function johnson_solid(index::Int)
   if haskey(_johnson_names, index)
     # code used for generation of loaded files can be found at:
     # https://github.com/dmg-lab/JohnsonSrc
-    vertices = load(joinpath(oscardir, "data", "JohnsonMatrices", string("j", index, ".mat")))
-    parent_field = base_ring(vertices)
-    return convex_hull(parent_field, vertices; non_redundant = true)
+    str_index = lpad(index, 2, '0')
+    filename = "j$str_index" * ".mrdi"
+    return load(joinpath(oscardir, "data", "JohnsonSolids", filename))
   end
   pmp = Polymake.polytope.johnson_solid(index)
   return polyhedron(pmp)
diff --git a/src/PolyhedralGeometry/helpers.jl b/src/PolyhedralGeometry/helpers.jl
index 21f481749b8d..061e45191959 100644
--- a/src/PolyhedralGeometry/helpers.jl
+++ b/src/PolyhedralGeometry/helpers.jl
@@ -122,29 +122,17 @@ matrix_for_polymake(x::Union{Oscar.ZZMatrix, Oscar.QQMatrix, AbstractMatrix}) =
 
 number_of_rows(x::SubArray{T, 2, U, V, W}) where {T, U, V, W} = size(x, 1)
 
-function Polymake.Matrix{Polymake.Rational}(x::Union{Oscar.QQMatrix,AbstractMatrix{Oscar.QQFieldElem}})
-    res = Polymake.Matrix{Polymake.Rational}(size(x)...)
-    for i in eachindex(x)
-        res[i] = x[i]
-    end
-    return res
-end
-
-function Polymake.Matrix{Polymake.OscarNumber}(x::Union{MatElem, AbstractMatrix{<:FieldElem}})
-    res = Polymake.Matrix{Polymake.OscarNumber}(size(x)...)
-    for i in eachindex(x)
-        res[i] = x[i]
-    end
-    return res
-end
-
 _isempty_halfspace(x::Pair{<:Union{Oscar.MatElem, AbstractMatrix}, Any}) = isempty(x[1])
 _isempty_halfspace(x) = isempty(x)
 
+function Polymake.Matrix{T}(x::Union{MatElem,AbstractMatrix{<:FieldElem}}) where T<:Union{Float64, Polymake.Rational, Polymake.Integer, Polymake.OscarNumber}
+    res = Polymake.Matrix{T}(size(x)...)
+    return res .= x
+end
 
-Base.convert(::Type{Polymake.QuadraticExtension{Polymake.Rational}}, x::QQFieldElem) = Polymake.QuadraticExtension(convert(Polymake.Rational, x))
+Base.convert(::Type{Polymake.Matrix{T}}, x::MatElem) where T = Polymake.Matrix{T}(x)
 
-Base.convert(T::Type{<:Polymake.Matrix}, x::Union{ZZMatrix,QQMatrix}) = Base.convert(T, Matrix(x))
+Base.convert(::Type{Polymake.QuadraticExtension{Polymake.Rational}}, x::QQFieldElem) = Polymake.QuadraticExtension(convert(Polymake.Rational, x))
 
 Base.convert(::Type{<:Polymake.Integer}, x::ZZRingElem) = GC.@preserve x return Polymake.new_integer_from_fmpz(x)
 
@@ -182,8 +170,6 @@ Base.convert(::Type{Polymake.OscarNumber}, x::FieldElem) = Polymake.OscarNumber(
 
 (::Type{T})(x::Polymake.OscarNumber) where T<:FieldElem = convert(T, Polymake.unwrap(x))
 
-Base.convert(::Type{Polymake.Matrix{Polymake.OscarNumber}}, x::MatElem{<:FieldElem}) = Polymake.Matrix{Polymake.OscarNumber}(x)
-
 (R::QQField)(x::Polymake.Rational) = convert(QQFieldElem, x)
 (Z::ZZRing)(x::Polymake.Rational) = convert(ZZRingElem, x)
 
@@ -202,12 +188,16 @@ end
 (F::Field)(x::Polymake.Rational) = F(QQ(x))
 (F::Field)(x::Polymake.OscarNumber) = F(Polymake.unwrap(x))
 
-Polymake.convert_to_pm_type(::Type{Oscar.ZZMatrix}) = Polymake.Matrix{Polymake.Integer}
-Polymake.convert_to_pm_type(::Type{Oscar.QQMatrix}) = Polymake.Matrix{Polymake.Rational}
-Polymake.convert_to_pm_type(::Type{Oscar.ZZRingElem}) = Polymake.Integer
-Polymake.convert_to_pm_type(::Type{Oscar.QQFieldElem}) = Polymake.Rational
+Polymake.convert_to_pm_type(::Type{ZZMatrix}) = Polymake.Matrix{Polymake.Integer}
+Polymake.convert_to_pm_type(::Type{QQMatrix}) = Polymake.Matrix{Polymake.Rational}
+Polymake.convert_to_pm_type(::Type{ZZRingElem}) = Polymake.Integer
+Polymake.convert_to_pm_type(::Type{QQFieldElem}) = Polymake.Rational
 Polymake.convert_to_pm_type(::Type{T}) where T<:FieldElem = Polymake.OscarNumber
 Polymake.convert_to_pm_type(::Type{<:Oscar.MatElem}) = Polymake.Matrix{Polymake.OscarNumber}
+Polymake.convert_to_pm_type(::Type{<:Graph{T}}) where T<:Union{Directed,Undirected} = Polymake.Graph{T}
+Polymake.convert_to_pm_type(::Type{<:MatElem{Float64}}) = Polymake.Matrix{Float64}
+
+Base.convert(::Type{<:Polymake.Graph{T}}, g::Graph{T}) where T<:Union{Directed,Undirected} = Oscar.pm_object(g)
 
 function remove_zero_rows(A::AbstractMatrix)
     A[findall(x->!iszero(x),collect(eachrow(A))),:]
diff --git a/src/PolyhedralGeometry/mixed_integer_linear_program.jl b/src/PolyhedralGeometry/mixed_integer_linear_program.jl
index b7715d2e9652..a4d0fcaa2287 100644
--- a/src/PolyhedralGeometry/mixed_integer_linear_program.jl
+++ b/src/PolyhedralGeometry/mixed_integer_linear_program.jl
@@ -2,15 +2,16 @@ struct MixedIntegerLinearProgram{T} <: PolyhedralObject{T}
   feasible_region::Polyhedron{T}
   polymake_milp::Polymake.BigObject
   convention::Symbol
+  parent_field::Field
 
   MixedIntegerLinearProgram{T}(
-    fr::Polyhedron{T}, milp::Polymake.BigObject, c::Symbol
-  ) where {T<:scalar_types} = new{T}(fr, milp, c)
+    fr::Polyhedron{T}, milp::Polymake.BigObject, c::Symbol, parent_field::Field
+  ) where {T<:scalar_types} = new{T}(fr, milp, c, parent_field)
 end
 
 # no default = `QQFieldElem` here; scalar type can be derived from the feasible region
 mixed_integer_linear_program(p::Polyhedron{T}, x...) where {T<:scalar_types} =
-  MixedIntegerLinearProgram{T}(p, x...)
+  MixedIntegerLinearProgram{T}(p, x..., coefficient_field(p))
 
 @doc raw"""
     mixed_integer_linear_program(P, c; integer_variables = [], k = 0, convention = :max)
@@ -45,10 +46,10 @@ function mixed_integer_linear_program(
     Polymake.attach(milp, "convention", "min")
   end
   Polymake.add(pm_object(P), "MILP", milp)
-  MixedIntegerLinearProgram{T}(P, milp, convention)
+  MixedIntegerLinearProgram{T}(P, milp, convention, coefficient_field(P))
 end
 
-mixed_integer_linear_program(
+function mixed_integer_linear_program(
   ::Type{T},
   A::Union{Oscar.MatElem,AbstractMatrix},
   b,
@@ -56,9 +57,13 @@ mixed_integer_linear_program(
   integer_variables=Vector{Int64}([]),
   k=0,
   convention=:max,
-) where {T<:scalar_types} = mixed_integer_linear_program(
-  polyhedron(T, A, b), c; integer_variables=integer_variables, k=k, convention=convention
-)
+  ) where {T<:scalar_types}
+  P = polyhedron(T, A, b)
+  return mixed_integer_linear_program(
+    P, c, coefficient_field(P);
+    integer_variables=integer_variables, k=k, convention=convention
+  )
+end
 
 pm_object(milp::MixedIntegerLinearProgram) = milp.polymake_milp
 
diff --git a/src/Serialization/Fields.jl b/src/Serialization/Fields.jl
index 9fa63fcf5600..6df50bdc2bcb 100644
--- a/src/Serialization/Fields.jl
+++ b/src/Serialization/Fields.jl
@@ -52,6 +52,10 @@ function load_object(s:: DeserializerState, ::Type{Field})
   return load_typed_object(s)
 end
 
+################################################################################
+# floats
+@register_serialization_type AbstractAlgebra.Floats{Float64} "Floats"
+
 ################################################################################
 # field of rationals (singleton type)
 @register_serialization_type QQField
diff --git a/src/Serialization/PolyhedralGeometry.jl b/src/Serialization/PolyhedralGeometry.jl
index 1d9132593f49..c16c4dc399b2 100644
--- a/src/Serialization/PolyhedralGeometry.jl
+++ b/src/Serialization/PolyhedralGeometry.jl
@@ -39,27 +39,51 @@ function save_type_params(s::SerializerState, obj::T) where T <: PolyhedralObjec
   end
 end
 
-function save_object(s::SerializerState, obj::PolyhedralObject)
+function save_object(s::SerializerState, obj::PolyhedralObject{S}) where S <: Union{QQFieldElem, Float64}
   save_object(s, pm_object(obj))
 end
 
+function save_object(s::SerializerState, obj::PolyhedralObject{<:FieldElem})
+  if typeof(obj) <: Union{MixedIntegerLinearProgram, LinearProgram}
+    T = typeof(obj)
+    error("Unsupported type $T for serialization")
+  end
+  save_data_dict(s) do
+    save_typed_object(s, _polyhedral_object_as_dict(obj))
+  end
+end
+
 function load_type_params(s::DeserializerState, ::Type{<:PolyhedralObject})
   return load_typed_object(s)
 end
 
-function load_object(s::DeserializerState, T::Type{<:PolyhedralObject}, field::Field) 
-  return  load_from_polymake(T{elem_type(field)}, Dict{Symbol, Any}(s.obj))
+function load_object(s::DeserializerState, T::Type{<:PolyhedralObject},
+                     field::U) where {U <: Union{QQField, AbstractAlgebra.Floats}}
+  return load_from_polymake(T{elem_type(field)}, Dict{Symbol, Any}(s.obj))
 end
 
 function load_object(s::DeserializerState, T::Type{<:PolyhedralObject{S}},
-                     field::Field) where S <: FieldElem
+    field::U) where {S <: Union{QQFieldElem, Float64}, U <: Union{QQField, AbstractAlgebra.Floats}}
   return load_from_polymake(T, Dict{Symbol, Any}(s.obj))
 end
 
+function load_object(s::DeserializerState, T::Type{<:PolyhedralObject}, field::Field)
+  polymake_dict = load_typed_object(s)
+  bigobject = _dict_to_bigobject(polymake_dict)
+  return T{elem_type(field)}(bigobject, field)
+end
+
+function load_object(s::DeserializerState, T::Type{<:PolyhedralObject{S}},
+                     field::Field) where S <: FieldElem
+  polymake_dict = load_typed_object(s)
+  bigobject = _dict_to_bigobject(polymake_dict)
+  return T(bigobject, field)
+end
+
 ##############################################################################
 @register_serialization_type LinearProgram uses_params
 
-function save_object(s::SerializerState, lp::LinearProgram)
+function save_object(s::SerializerState, lp::LinearProgram{QQFieldElem})
   lpcoeffs = lp.polymake_lp.LINEAR_OBJECTIVE
   serialized = Polymake.call_function(Symbol("Core::Serializer"), :serialize, lpcoeffs)
   jsonstr = Polymake.call_function(:common, :encode_json, serialized)
@@ -70,7 +94,7 @@ function save_object(s::SerializerState, lp::LinearProgram)
   end
 end
 
-function load_object(s::DeserializerState, ::Type{<:LinearProgram}, field::Field)
+function load_object(s::DeserializerState, ::Type{<:LinearProgram}, field::QQField)
   coeff_type = elem_type(field)
   fr = load_object(s, Polyhedron, field, :feasible_region)
   conv = load_object(s, String, :convention)
@@ -92,7 +116,7 @@ end
 ##############################################################################
 @register_serialization_type MixedIntegerLinearProgram uses_params
 
-function save_object(s::SerializerState, milp::MixedIntegerLinearProgram)
+function save_object(s::SerializerState, milp::MixedIntegerLinearProgram{QQFieldElem})
   milp_coeffs = milp.polymake_milp.LINEAR_OBJECTIVE
   int_vars = milp.polymake_milp.INTEGER_VARIABLES
   coeffs_serialized = Polymake.call_function(
@@ -109,7 +133,7 @@ function save_object(s::SerializerState, milp::MixedIntegerLinearProgram)
   end
 end
 
-function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram}, field::Field) 
+function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram}, field::QQField) 
   fr = load_object(s, Polyhedron, field, :feasible_region)
   conv = load_object(s, String, :convention)
   milp_coeffs = load_node(s, :milp_coeffs) do coeffs
@@ -137,7 +161,7 @@ function load_object(s::DeserializerState, ::Type{<: MixedIntegerLinearProgram},
   end
   lp = Polymake._lookup_multi(pm_object(fr), "MILP", index-1)
   T = elem_type(field)
-  return MixedIntegerLinearProgram{T}(fr, lp, Symbol(conv))
+  return MixedIntegerLinearProgram{T}(fr, lp, Symbol(conv), field)
 end
 
 # use generic serialization for the other types:
diff --git a/src/Serialization/containers.jl b/src/Serialization/containers.jl
index 6f656c6f11d9..705623614bed 100644
--- a/src/Serialization/containers.jl
+++ b/src/Serialization/containers.jl
@@ -9,8 +9,8 @@ function save_type_params(s::SerializerState, obj::S) where {T, S <:MatVecType{T
   save_data_dict(s) do
     save_object(s, encode_type(S), :name)
     if serialize_with_params(T) && !isempty(obj)
-      if hasmethod(parent, (T,))
-        parents = map(parent, obj)
+      if !(T <: MatVecType) && hasmethod(parent, (T,))
+        parents = parent.(obj)
         parents_all_equal = all(map(x -> isequal(first(parents), x), parents))
         @req parents_all_equal "Not all parents of Vector or Matrix entries are the same, consider using a Tuple"
       end
@@ -84,7 +84,8 @@ function load_object(s::DeserializerState, ::Type{<: Vector}, params::Tuple)
       return T[]
     else
       loaded_v = []
-      for i in 1:length(v)
+      len = length(v)
+      for i in 1:len
         load_node(s, i) do _
           push!(loaded_v, load_object(s, T, params[2]))
         end
@@ -114,7 +115,7 @@ function save_type_params(s::SerializerState, tup::T) where T <: Tuple
   save_data_dict(s) do
     save_object(s, encode_type(Tuple), :name)
     n = fieldcount(T)
-    save_data_array(s, :params) do 
+    save_data_array(s, :params) do
       for i in 1:n
         U = fieldtype(T, i)
         if serialize_with_params(U)
@@ -141,7 +142,7 @@ function load_type_params(s::DeserializerState, ::Type{Tuple})
 end
 
 function save_object(s::SerializerState, obj::Tuple)
-  save_data_array(s) do 
+  save_data_array(s) do
     for entry in obj
       if serialize_with_id(typeof(entry))
         ref = save_as_ref(s, entry)
@@ -176,7 +177,7 @@ function save_type_params(s::SerializerState, obj::T) where T <: NamedTuple
   save_data_dict(s) do
     save_object(s, encode_type(NamedTuple), :name)
     save_data_dict(s, :params) do
-      save_data_array(s, :tuple_params) do 
+      save_data_array(s, :tuple_params) do
         for (i, value) in enumerate(values(obj))
           U = fieldtype(T, i)
           if serialize_with_params(U)
@@ -221,7 +222,7 @@ end
 ################################################################################
 # Saving and loading matrices
 @register_serialization_type Matrix uses_params
-  
+
 function save_object(s::SerializerState, mat::Matrix)
   m, n = size(mat)
   save_data_array(s) do
@@ -236,8 +237,9 @@ function load_object(s::DeserializerState, ::Type{<:Matrix}, params::Type)
     if isempty(entries)
       return zero_matrix(parent_type(params)(), 0, 0)
     end
+    len = length(entries)
     m = reduce(vcat, [
-      permutedims(load_object(s, Vector, params, i)) for i in 1:length(entries)
+      permutedims(load_object(s, Vector, params, i)) for i in 1:len
         ])
     return Matrix{params}(m)
   end
@@ -245,9 +247,169 @@ end
 
 function load_object(s::DeserializerState, ::Type{<:Matrix}, params::Tuple)
   load_node(s) do entries
+    if isempty(entries)
+      return params[1][]
+    end
+
+    len = length(entries)
     m = reduce(vcat, [
-      permutedims(load_object(s, Vector, params, i)) for i in 1:length(entries)
+      permutedims(load_object(s, Vector, params, i)) for i in 1:len
         ])
     return Matrix{params[1]}(m)
   end
 end
+
+################################################################################
+# Saving and loading dicts
+@register_serialization_type Dict uses_params
+
+function save_type_params(s::SerializerState, obj::Dict{S, T}) where {S <: Union{Symbol, String, Int}, T}
+  save_data_dict(s) do
+    save_object(s, encode_type(Dict), :name)
+    save_data_dict(s, :params) do
+      save_object(s, encode_type(S), :key_type)
+      for (k, v) in obj
+        U = typeof(v)
+        if serialize_with_params(U)
+          save_type_params(s, v, Symbol(k))
+        else
+          save_object(s, encode_type(U), Symbol(k))
+        end
+      end
+    end
+  end
+end
+
+function load_type_params(s::DeserializerState, ::Type{<:Dict})
+  params_dict = Dict{Symbol, Any}()
+  for (k, _) in s.obj
+    load_node(s, k) do _
+      value_type = decode_type(s)
+
+      if serialize_with_params(value_type)
+        params_dict[k] = Dict{Symbol, Any}(
+          type_key => value_type,
+          :params => load_params_node(s)
+        )
+      else
+        params_dict[k] = value_type
+      end
+    end
+  end
+  return params_dict
+end
+
+function save_object(s::SerializerState, obj::Dict{S, T}) where {S <: Union{Symbol, String, Int}, T}
+  save_data_dict(s) do
+    for (k, v) in obj
+      save_object(s, v, Symbol(k))
+    end
+  end
+end
+
+function load_object(s::DeserializerState, ::Type{<:Dict}, params::Dict{Symbol, Any})
+  key_type = params[:key_type]
+
+  dict = Dict{key_type, Any}()
+  for (k, _) in s.obj
+    if k == :key_type
+      continue
+    end
+
+    if key_type == Int
+      key = parse(Int, string(k))
+    else
+      key = key_type(k)
+    end
+
+    if params[k] isa Type
+      dict[key] = load_object(s, params[k], k)
+    else
+      dict[key] = load_object(s, params[k][type_key], params[k][:params], k)
+    end
+  end
+
+  return dict
+end
+
+################################################################################
+# Saving and loading sets
+@register_serialization_type Set uses_params
+
+function save_type_params(s::SerializerState, obj::Set{T}) where T
+  save_data_dict(s) do
+    save_object(s, encode_type(Set), :name)
+    if serialize_with_params(T) && !isempty(obj)
+        save_type_params(s, first(obj), :params)
+      else
+        save_object(s, encode_type(T), :params)
+      end
+  end
+end
+
+function load_type_params(s::DeserializerState, ::Type{<:Set})
+  T = decode_type(s)
+  if serialize_with_params(T) && haskey(s, :params)
+    params = load_params_node(s)
+    return (T, params)
+  end
+  return T
+end
+
+function save_object(s::SerializerState, x::Set)
+  save_data_array(s) do
+    for elem in x
+      if serialize_with_id(typeof(elem))
+        ref = save_as_ref(s, elem)
+        save_object(s, ref)
+      else
+        save_object(s, elem)
+      end
+    end
+  end
+end
+
+function load_object(s::DeserializerState, ::Type{<: Set}, params::Any)
+  load_node(s) do v
+    if serialize_with_id(params)
+      loaded_v = params[load_ref(s, x) for x in v]
+    else
+      loaded_v = params[]
+      for (i, entry) in enumerate(v)
+        push!(loaded_v, load_object(s, params, i))
+      end
+    end
+    return Set(loaded_v)
+  end
+end
+
+# handles nested
+function load_object(s::DeserializerState, ::Type{<: Set}, params::Tuple)
+  T = params[1]
+  load_node(s) do v
+    if isempty(v)
+      return Set{T}()
+    else
+      loaded_v = Set{T}()
+      len = length(v)
+      for i in 1:len
+        load_node(s, i) do _
+          push!(loaded_v, load_object(s, T, params[2]))
+        end
+      end
+      return Set{typeof(first(loaded_v))}(loaded_v)
+    end
+  end
+end
+
+function load_object(s::DeserializerState, ::Type{<: Set}, params::Ring)
+  T = elem_type(params)
+  loaded_entries = load_array_node(s) do _
+    if serialize_with_params(T)
+      return load_object(s, T, params)
+    else
+      return load_object(s, T)
+    end
+  end
+  return Set{T}(loaded_entries)
+end
diff --git a/src/Serialization/main.jl b/src/Serialization/main.jl
index 6abfe7d2dd25..0b262856b958 100644
--- a/src/Serialization/main.jl
+++ b/src/Serialization/main.jl
@@ -42,7 +42,7 @@ function version_number(v_number::String)
   return VersionNumber(v_number)
 end
 
-# needed for older versions 
+# needed for older versions
 function version_number(dict::Dict)
   return VersionNumber(dict[:major], dict[:minor], dict[:patch])
 end
@@ -97,7 +97,7 @@ function decode_type(s::DeserializerState)
       error("unsupported type '$unsupported_type' for decoding")
     end
   end
-  
+
   if type_key in keys(s.obj)
     return load_node(s, type_key) do _
       decode_type(s)
@@ -175,7 +175,7 @@ function save_typed_object(s::SerializerState, x::T, key::Symbol) where T
     ref = save_as_ref(s, x)
     save_object(s, ref)
   else
-    save_data_dict(s) do 
+    save_data_dict(s) do
       save_typed_object(s, x)
     end
   end
@@ -202,7 +202,11 @@ function load_typed_object(s::DeserializerState; override_params::Any = nothing)
   if Base.issingletontype(T) && return T()
   elseif serialize_with_params(T)
     if !isnothing(override_params)
-      params = override_params
+      if override_params isa Dict
+        error("Unsupported override type")
+      else
+        params = override_params
+      end
     else
       # depending on the type, :params is either an object to be loaded or a
       # dict with keys and object values to be loaded
@@ -284,8 +288,10 @@ import Distributed.AbstractSerializer
 # add these here so that the proper errors are thrown
 # when the type hasn't been registered
 serialize_with_id(::Type) = false
+serialize_with_id(obj::Any) = false
 serialize_with_params(::Type) = false
 
+
 function register_serialization_type(ex::Any, str::String, uses_id::Bool, uses_params::Bool)
   return esc(
     quote
@@ -304,12 +310,13 @@ function register_serialization_type(ex::Any, str::String, uses_id::Bool, uses_p
       # Types like ZZ, QQ, and ZZ/nZZ do not require ids since there is no syntactic
       # ambiguities in their encodings.
 
-      serialize_with_id(obj::T) where T <: $ex = $uses_id 
+      serialize_with_id(obj::T) where T <: $ex = $uses_id
       serialize_with_id(T::Type{<:$ex}) = $uses_id
       serialize_with_params(T::Type{<:$ex}) = $uses_params
 
       # only extend serialize on non std julia types
-      if !($ex <: Union{Number, String, Bool, Symbol, Vector, Tuple, Matrix, NamedTuple})
+      non_oscar_types = Union{Number, String, Bool, Symbol, Vector, Tuple, Matrix, NamedTuple, Dict, Set}
+      if !($ex <: non_oscar_types)
         function serialize(s::AbstractSerializer, obj::T) where T <: $ex
           serialize_type(s, T)
           save(s.io, obj; serializer_type=IPCSerializer)
@@ -426,9 +433,9 @@ function save(io::IO, obj::T; metadata::Union{MetaData, Nothing}=nothing,
         global_serializer_state.id_to_obj[ref] = obj
       end
       save_object(s, string(ref), :id)
-      
+
     end
-    
+
     # this should be handled by serializers in a later commit / PR
     if !isempty(s.refs) && serializer_type == JSONSerializer
       save_data_dict(s, refs_key) do
@@ -441,7 +448,7 @@ function save(io::IO, obj::T; metadata::Union{MetaData, Nothing}=nothing,
         end
       end
     end
-    
+
     if !isnothing(metadata)
       save_json(s, json(metadata), :meta)
     end
@@ -483,7 +490,7 @@ See [`save`](@ref).
 
 ```jldoctest
 julia> save("/tmp/fourtitwo.json", 42);
-  
+
 julia> load("/tmp/fourtitwo.json")
 42
 
@@ -611,4 +618,3 @@ function load(filename::String; params::Any = nothing, type::Any = nothing)
     return load(file; params=params, type=type)
   end
 end
-
diff --git a/src/Serialization/polymake.jl b/src/Serialization/polymake.jl
index 59246167da25..4b876581d5e3 100644
--- a/src/Serialization/polymake.jl
+++ b/src/Serialization/polymake.jl
@@ -35,9 +35,14 @@ const polymake2OscarTypes = Dict{String, Type}([
 function load_from_polymake(::Type{T}, jsondict::Dict{Symbol, Any}) where {
   T<:Union{Cone{<:scalar_types}, Polyhedron{<:scalar_types}, PolyhedralFan{<:scalar_types}, 
            PolyhedralComplex{<:scalar_types}, SubdivisionOfPoints{<:scalar_types}, SimplicialComplex}}
-  
   inner_object = Polymake.call_function(:common, :deserialize_json_string, json(jsondict))
-  return T(inner_object)
+  if T <: PolyhedralObject{QQFieldElem}
+     return T(inner_object)
+   elseif T <: PolyhedralObject{Float64}
+     return T(inner_object, AbstractAlgebra.Floats{Float64}())
+   else
+      error("Unsupported object type $T for loading polymake object")
+   end
 end
 
 
@@ -64,3 +69,85 @@ function load_from_polymake(jsondict::Dict{Symbol, Any})
   end
 end
 
+_pmdata_for_oscar(bo::Polymake.BigObject, coeff::Field) = _bigobject_to_dict(bo, coeff)
+
+_pmdata_for_oscar(::Nothing, coeff::Field) = nothing
+_pmdata_for_oscar(v::Union{Bool,Int64,Float64,String}, coeff::Field) = v
+if Polymake.CxxWrap.CxxLong != Int64
+  _pmdata_for_oscar(i::Polymake.CxxWrap.CxxLong, coeff::Field) = Int64(i)
+end
+
+_pmdata_for_oscar(im::IncidenceMatrix, coeff::Field) = im
+
+_pmdata_for_oscar(g::Polymake.Graph{T}, coeff::Field) where T = Graph{T}(g)
+
+_pmdata_for_oscar(m::Polymake.Matrix, coeff::Field) = matrix(coeff, m)
+_pmdata_for_oscar(m::Polymake.Matrix{<:Polymake.Integer}, coeff::Field) = matrix(ZZ, m)
+_pmdata_for_oscar(m::Polymake.Matrix{<:Polymake.Rational}, coeff::Field) = matrix(QQ, m)
+
+_pmdata_for_oscar(m::Polymake.SparseMatrix, coeff::Field) = _pmdata_for_oscar(Polymake.common.dense(m), coeff)
+
+_pmdata_for_oscar(v::Polymake.Vector, coeff::Field) = collect(elem_type(coeff), map(coeff, v))
+_pmdata_for_oscar(v::Polymake.Vector{<:Polymake.Integer}, coeff::Field) = collect(ZZRingElem, map(ZZ, v))
+_pmdata_for_oscar(v::Polymake.Vector{<:Polymake.Rational}, coeff::Field) = collect(QQFieldElem, map(QQ, v))
+
+_pmdata_for_oscar(v::Polymake.SparseVector, coeff::Field) = _pmdata_for_oscar(Polymake.common.dense(v), coeff)
+
+_pmdata_for_oscar(s::Polymake.Integer, coeff::Field) = ZZ(s)
+_pmdata_for_oscar(s::Polymake.Rational, coeff::Field) = QQ(s)
+_pmdata_for_oscar(s::Polymake.OscarNumber, coeff::Field) = coeff(s)
+
+_pmdata_for_oscar(s::Polymake.CxxWrap.StdString, coeff::Field) = String(s)
+
+_pmdata_for_oscar(a::Polymake.Array, coeff::Field) = [_pmdata_for_oscar(e, coeff) for e in a]
+_pmdata_for_oscar(s::Polymake.Set, coeff::Field) = Set(_pmdata_for_oscar(e, coeff) for e in s)
+
+
+function _bigobject_to_dict(bo::Polymake.BigObject, coeff::Field)
+  data = Dict{String,Any}()
+  for pname in Polymake.list_properties(bo)
+    p = Polymake.give(bo, pname)
+    if p isa Polymake.PropertyValue
+      @debug "missing c++ mapping: skipping $pname of type $(Polymake.typeinfo_string(p, true))"
+    else
+      try
+        obj = _pmdata_for_oscar(p, coeff)
+        data[pname] = obj
+      catch e
+        if e isa MethodError
+          @debug "failed to convert $pname of type $(typeof(p)) to Oscar, skipping"
+        else
+          rethrow(e)
+        end
+      end
+    end
+  end
+  data
+end
+
+function _polyhedral_object_as_dict(x::Oscar.PolyhedralObjectUnion)
+  bo = Oscar.pm_object(x)
+  data = _bigobject_to_dict(bo, coefficient_field(x))
+  data["_type"] = Polymake.bigobject_qualifiedname(bo)
+  data["_coeff"] = coefficient_field(x)
+  return data
+end
+
+function _load_bigobject_from_dict!(obj::Polymake.BigObject, dict::Dict, parent_key::String="")
+  for (k, v) in dict
+    key_str = parent_key == "" ? k : parent_key * "." * k
+    first(k) == '_' && continue
+
+    if v isa Dict
+      _load_bigobject_from_dict!(obj, v, key_str)
+    else
+      Polymake.take(obj, key_str, convert(Polymake.PolymakeType, v))
+    end
+  end
+end
+
+function _dict_to_bigobject(dict::Dict{String, Any})
+  obj = Polymake.BigObject(Polymake.BigObjectType(dict["_type"]))
+  _load_bigobject_from_dict!(obj, dict)
+  return obj
+end
diff --git a/src/Serialization/serializers.jl b/src/Serialization/serializers.jl
index 62e6d446d90e..0a2df3d52c14 100644
--- a/src/Serialization/serializers.jl
+++ b/src/Serialization/serializers.jl
@@ -231,7 +231,7 @@ function deserializer_open(io::IO, T::Type{IPCSerializer})
   # Using a JSON3.Object from JSON3 version 1.13.2 causes
   # @everywhere using Oscar
   # to hang. So we use a Dict here for now.
-  
+
   obj = JSON.parse(io, dicttype=Dict{Symbol, Any})
   return T(DeserializerState(obj, nothing, nothing))
 end
diff --git a/test/PolyhedralGeometry/polyhedron.jl b/test/PolyhedralGeometry/polyhedron.jl
index 18e41a83a6be..c2f3000ec46f 100644
--- a/test/PolyhedralGeometry/polyhedron.jl
+++ b/test/PolyhedralGeometry/polyhedron.jl
@@ -585,11 +585,9 @@ end
 @testset "Johnson solids" begin
   
   for i in keys(Oscar._johnson_names)
-    
     j = johnson_solid(i)
     @test j isa Polyhedron{<:EmbeddedNumFieldElem}
     @test Polymake.polytope.isomorphic(Oscar.pm_object(j), Polymake.polytope.johnson_solid(i))
-    
   end
   
 end
diff --git a/test/Serialization/PolyhedralGeometry.jl b/test/Serialization/PolyhedralGeometry.jl
index f7782ba246f5..2b80ea0de0e6 100644
--- a/test/Serialization/PolyhedralGeometry.jl
+++ b/test/Serialization/PolyhedralGeometry.jl
@@ -1,69 +1,96 @@
 using Oscar: _integer_variables
 @testset "PolyhedralGeometry" begin
-    
+  Qx, x = QQ[:x]
+  F, a = embedded_number_field(x^2 - 2, -1.0)
+
     mktempdir() do path
         @testset "Graph" begin
             G = complete_graph(4)
             test_save_load_roundtrip(path, G) do loaded
-              @test loaded isa Graph{Undirected}
-              @test Base.propertynames(G) == Base.propertynames(loaded)
               @test n_vertices(G) == n_vertices(loaded)
               @test n_edges(G) == n_edges(loaded)
             end
         end
 
         @testset "Cone" begin
-            C = positive_hull([1 0; 0 1])
-            test_save_load_roundtrip(path, C) do loaded
-              @test loaded isa Cone
-              @test Base.propertynames(C) == Base.propertynames(loaded)
-              @test n_rays(C) == n_rays(loaded)
-              @test dim(C) == dim(loaded)
-              @test C == loaded
-            end
+          C = positive_hull([1 0; 0 1])
+          test_save_load_roundtrip(path, C) do loaded
+            @test n_rays(C) == n_rays(loaded)
+            @test dim(C) == dim(loaded)
+            @test C == loaded
+          end
+
+          CF = positive_hull(F, [F(1) F(0); F(0) F(1)])
+          test_save_load_roundtrip(path, CF) do loaded
+            @test n_rays(CF) == n_rays(loaded)
+            @test dim(CF) == dim(loaded)
+            @test CF == loaded
+          end
         end
 
         @testset "Polyhedron" begin
-            square = cube(2)
-            test_save_load_roundtrip(path, square) do loaded
-              @test loaded isa Polyhedron
-              @test Base.propertynames(square) == Base.propertynames(loaded)
-              @test n_vertices(square) == n_vertices(loaded)
-              @test dim(square) == dim(loaded)
-              @test square == loaded
-            end
+          square = cube(2)
+          test_save_load_roundtrip(path, square) do loaded
+            @test n_vertices(square) == n_vertices(loaded)
+            @test dim(square) == dim(loaded)
+            @test square == loaded
+          end
+          
+          d_hedron = dodecahedron()
+          facets(d_hedron)
+          vertices(d_hedron)
+
+          dict_ps = Dict{String, Any}(
+            "unprecise" => polyhedron(
+              Polymake.common.convert_to{Float64}(Oscar.pm_object(d_hedron))
+            ),
+            "precise" => d_hedron
+          )
+
+          test_save_load_roundtrip(path, dict_ps) do loaded
+            @test dict_ps["precise"] == loaded["precise"]
+          end
         end
 
         @testset "PolyhedralComplex" begin
-            IM = IncidenceMatrix([[1,2,3],[1,3,4]])
-            vr = [0 0; 1 0; 1 1; 0 1]
-            PC = polyhedral_complex(IM, vr)
-            test_save_load_roundtrip(path, PC) do loaded
-              @test loaded isa PolyhedralComplex
-              @test Base.propertynames(PC) == Base.propertynames(loaded)
-              @test n_rays(PC) == n_rays(loaded)
-              @test number_of_maximal_polyhedra(PC) == number_of_maximal_polyhedra(loaded)
-              @test dim(PC) == dim(loaded)
-            end
+          IM = IncidenceMatrix([[1,2,3],[1,3,4]])
+          vr = [0 0; 1 0; 1 1; 0 1]
+          PC = polyhedral_complex(IM, vr)
+          test_save_load_roundtrip(path, PC) do loaded
+            @test n_rays(PC) == n_rays(loaded)
+            @test number_of_maximal_polyhedra(PC) == number_of_maximal_polyhedra(loaded)
+            @test dim(PC) == dim(loaded)
+          end
+
+          vr_F = F.([0 0; 1 0; 1 1; 0 1])
+          PC_F = polyhedral_complex(IM, vr_F)
+          test_save_load_roundtrip(path, PC_F) do loaded
+            @test n_rays(PC_F) == n_rays(loaded)
+            @test number_of_maximal_polyhedra(PC_F) == number_of_maximal_polyhedra(loaded)
+            @test dim(PC_F) == dim(loaded)
+          end
         end
 
         @testset "PolyhedralFan" begin
-            nfsquare = normal_fan(cube(2))
-            test_save_load_roundtrip(path, nfsquare) do loaded
-              @test loaded isa PolyhedralFan
-              @test Base.propertynames(nfsquare) == Base.propertynames(loaded)
-              @test n_rays(nfsquare) == n_rays(loaded)
-              @test number_of_maximal_cones(nfsquare) == number_of_maximal_cones(loaded)
-              @test dim(nfsquare) == dim(loaded)
-            end
+          nfsquare = normal_fan(cube(2))
+          test_save_load_roundtrip(path, nfsquare) do loaded
+            @test n_rays(nfsquare) == n_rays(loaded)
+            @test number_of_maximal_cones(nfsquare) == number_of_maximal_cones(loaded)
+            @test dim(nfsquare) == dim(loaded)
+          end
+
+          nfdodecahedron = normal_fan(dodecahedron())
+          test_save_load_roundtrip(path, nfdodecahedron) do loaded
+            @test n_rays(nfdodecahedron) == n_rays(loaded)
+            @test number_of_maximal_cones(nfdodecahedron) == number_of_maximal_cones(loaded)
+            @test dim(nfdodecahedron) == dim(loaded)
+          end
         end
 
         @testset "LinearProgram" begin
             P = cube(3)
             LP = linear_program(P,[3,-2,4];k=2,convention = :min)
             test_save_load_roundtrip(path, LP) do loaded
-              @test loaded isa LinearProgram
-              @test Base.propertynames(LP) == Base.propertynames(loaded)
               @test objective_function(LP) == objective_function(loaded)
               @test feasible_region(LP) == feasible_region(loaded)
             end
@@ -79,8 +106,6 @@ using Oscar: _integer_variables
                 integer_variables=[1, 2]
             )
             test_save_load_roundtrip(path, MILP) do loaded
-              @test loaded isa MixedIntegerLinearProgram
-              @test Base.propertynames(MILP) == Base.propertynames(loaded)
               @test objective_function(MILP) == objective_function(loaded)
               @test feasible_region(MILP) == feasible_region(loaded)
               @test Oscar._integer_variables(MILP) == Oscar._integer_variables(loaded)
@@ -88,27 +113,28 @@ using Oscar: _integer_variables
         end
 
         @testset "SubdivisionOfPoints" begin
-            moaepts = [4 0 0; 0 4 0; 0 0 4; 2 1 1; 1 2 1; 1 1 2]
-            moaeimnonreg0 = IncidenceMatrix([[4,5,6],[1,4,2],[2,4,5],[2,3,5],[3,5,6],[1,3,6],[1,4,6]])
-            MOAE = subdivision_of_points(moaepts, moaeimnonreg0)
-            test_save_load_roundtrip(path, MOAE) do loaded
-              @test loaded isa SubdivisionOfPoints
-              @test Base.propertynames(MOAE) == Base.propertynames(loaded)
-              @test number_of_maximal_cells(MOAE) == number_of_maximal_cells(loaded)
-              @test number_of_points(MOAE) == number_of_points(loaded)
-            end
-        end
+          moaepts = [4 0 0; 0 4 0; 0 0 4; 2 1 1; 1 2 1; 1 1 2]
+          moaeimnonreg0 = IncidenceMatrix([[4,5,6],[1,4,2],[2,4,5],[2,3,5],[3,5,6],[1,3,6],[1,4,6]])
+          MOAE = subdivision_of_points(moaepts, moaeimnonreg0)
+          test_save_load_roundtrip(path, MOAE) do loaded
+            @test number_of_maximal_cells(MOAE) == number_of_maximal_cells(loaded)
+            @test number_of_points(MOAE) == number_of_points(loaded)
+          end
 
+          MOAEF = subdivision_of_points(F, F.(moaepts), moaeimnonreg0)
+          test_save_load_roundtrip(path, MOAEF) do loaded
+            @test number_of_maximal_cells(MOAEF) == number_of_maximal_cells(loaded)
+            @test number_of_points(MOAEF) == number_of_points(loaded)
+          end
+        end
 
         @testset "SimplicialComplex" begin
             cpp = complex_projective_plane()
             test_save_load_roundtrip(path, cpp) do loaded
-              @test loaded isa SimplicialComplex
               @test Base.propertynames(cpp) == Base.propertynames(loaded)
               @test euler_characteristic(cpp) == euler_characteristic(loaded)
               @test n_vertices(cpp) == n_vertices(loaded)
             end
         end
     end
-
 end
diff --git a/test/Serialization/containers.jl b/test/Serialization/containers.jl
index 9907031c8ccd..37bdd31b8eff 100644
--- a/test/Serialization/containers.jl
+++ b/test/Serialization/containers.jl
@@ -105,7 +105,7 @@
         @test original == loaded
       end
     end
-
+    
     @testset "(de)serialization NamedTuple{$(S), $(T)}" for (S, T) in
       (
         (UInt, UInt128), (UInt16, UInt32), (UInt64, UInt8),
@@ -119,6 +119,37 @@
       end
     end
 
+    @testset "(de)serialization Dict{$S, Any}" for (S, keys) in
+      (
+        (String, ["a", "b"]), (Int, [1, 2]), (Symbol, [:a, :b])
+      )
+      Qx, x = QQ[:x]
+      p = x^2 + 1
+      original = Dict(keys[1] => cube(:2), keys[2] => p)
+      test_save_load_roundtrip(path, original) do loaded
+        @test original == loaded
+      end
+    end
+
+    @testset "Testing (de)serialization of Set" begin
+      original = Set([Set([1, 2])])
+      test_save_load_roundtrip(path, original) do loaded
+        @test original == loaded
+      end
+
+      Qx, x = QQ[:x]
+      p = x^2 + 1
+      q = x
+      original = Set([p, q])
+      test_save_load_roundtrip(path, original) do loaded
+        @test original == loaded
+      end
+
+      test_save_load_roundtrip(path, original; params=Qx) do loaded
+        @test original == loaded
+      end
+    end
+
     @testset "Test for backwards compatibility" begin
       loaded_container = load(joinpath(@__DIR__, "old-containers.json"))
       @test loaded_container == (r = QQFieldElem(1, 2), m = QQFieldElem[1//2 1; 0 1], t = (1, 2, 3))