Example: Normal fan of dodecahedron
Profiles: OSCAR v1.0, OSCAR v1.1, OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8
Construct the normal fan of a dodecahedron and compute maximal-cone facets.
Related Specification
Systems
Oscar.jl
Generate code (generate.jl) [ edit ]
using Oscar
obj = normal_fan(dodecahedron())
Polymake.give(Oscar.pm_object(obj), :MAXIMAL_CONES_FACETS)
save("data.mrdi", obj)
Data outputs
Profiles: OSCAR v1.0
Data file: data.mrdi
{
"_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.0.5"]},
"_type": {"name": "PolyhedralFan", "params": "ee689053-9468-41a5-95bc-8e76ae61bd73"},
"data": {
"_type": {
"name": "Dict",
"params": {
"key_type": "String",
"FAN_DIM": "Base.Int",
"REGULAR": "Bool",
"LINEALITY_SPACE": {"name": "MatElem", "params": "ffe1bae3-b384-44a9-a574-b9c4afd3ec91"},
"_coeff": "EmbeddedNumField",
"FAN_AMBIENT_DIM": "Base.Int",
"_type": "String",
"PSEUDO_REGULAR": "Bool",
"LINEAR_SPAN_NORMALS": {"name": "MatElem", "params": "ffe1bae3-b384-44a9-a574-b9c4afd3ec91"},
"MAXIMAL_CONES_FACETS": {"name": "Matrix", "params": "Base.Int"},
"MAXIMAL_CONES": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"MAXIMAL_CONES_LINEAR_SPAN_NORMALS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"RAYS": {"name": "MatElem", "params": "0478086e-10f6-4d36-a0f9-354d30b130dd"},
"COMPLETE": "Bool",
"FACET_NORMALS": {"name": "MatElem", "params": "aaf77b9d-df0a-4e5e-9169-446f9f656271"},
"GROUP": {
"name": "Dict",
"params": {
"key_type": "String",
"RAYS_ACTION": {
"name": "Dict",
"params": {
"key_type": "String",
"GENERATORS": {"name": "Vector", "params": {"name": "Vector", "params": "Base.Int"}}
}
}
}
}
}
},
"data": {
"FAN_DIM": "3",
"REGULAR": "true",
"LINEALITY_SPACE": [],
"_coeff": {
"num_field": "3d20d31c-f11f-482f-aaf9-164ff355c054",
"embedding": "00a2c7d1-3560-4dcc-8b75-16ea45bac968"
},
"FAN_AMBIENT_DIM": "3",
"_type": "fan::PolyhedralFan<OscarNumber>",
"PSEUDO_REGULAR": "true",
"LINEAR_SPAN_NORMALS": [],
"MAXIMAL_CONES_FACETS": [
["1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "-1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "0", "-1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "0", "0", "-1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0"],
["-1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0"],
["0", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "0", "1", "0", "0", "0"],
["0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0"],
["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "-1", "0", "0"],
["0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "1"],
["0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "0", "0", "0", "0", "-1"],
["0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "0", "0", "1"],
["0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "-1", "-1"],
["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "0", "0"],
["0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0"],
["0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "-1", "0", "0", "0"],
["1", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "0", "0"],
["0", "0", "0", "1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0"],
["0", "0", "1", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "1", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["-1", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"]
],
"MAXIMAL_CONES": {
"_ns": {"polymake": ["https://polymake.org", "4.11"]},
"data": [
[0, 1, 2],
[1, 2, 5],
[0, 1, 6],
[1, 5, 7],
[0, 2, 4],
[1, 6, 7],
[2, 5, 9],
[2, 4, 9],
[0, 6, 10],
[0, 4, 10],
[3, 5, 7],
[3, 5, 9],
[6, 7, 8],
[6, 8, 10],
[4, 9, 11],
[3, 7, 8],
[4, 10, 11],
[3, 9, 11],
[8, 10, 11],
[3, 8, 11],
{"cols": 12}
],
"_type": "common::IncidenceMatrix<NonSymmetric>"
},
"MAXIMAL_CONES_LINEAR_SPAN_NORMALS": {
"_type": "common::IncidenceMatrix<NonSymmetric>",
"_ns": {"polymake": ["https://polymake.org", "4.11"]},
"data": [
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
{"cols": 0}
]
},
"RAYS": [
[[["0", "-1"]], [["0", "1//2"], ["1", "-1//2"]], []],
[[], [["0", "-1"]], [["0", "1//2"], ["1", "-1//2"]]],
[[], [["0", "-1"]], [["0", "-1//2"], ["1", "1//2"]]],
[[["0", "1"]], [["0", "-1//2"], ["1", "1//2"]], []],
[[["0", "-1"]], [], [["0", "1//2"], ["1", "1//2"]]],
[[["0", "1"]], [["0", "1//2"], ["1", "-1//2"]], []],
[[["0", "-1"]], [], [["0", "-1//2"], ["1", "-1//2"]]],
[[["0", "1"]], [], [["0", "-1//2"], ["1", "-1//2"]]],
[[], [["0", "1"]], [["0", "1//2"], ["1", "-1//2"]]],
[[["0", "1"]], [], [["0", "1//2"], ["1", "1//2"]]],
[[["0", "-1"]], [["0", "-1//2"], ["1", "1//2"]], []],
[[], [["0", "1"]], [["0", "-1//2"], ["1", "1//2"]]]
],
"COMPLETE": "true",
"FACET_NORMALS": [
[[["0", "3//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1"]], [], []],
[[["0", "3//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-3//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-3//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[], [["0", "-1"]], []],
[[["0", "1//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "1"]]],
[[], [], [["0", "-1"]]]
],
"GROUP": {
"RAYS_ACTION": {
"GENERATORS": [
["5", "1", "2", "10", "9", "0", "7", "6", "8", "4", "3", "11"],
["2", "1", "0", "8", "4", "6", "5", "7", "3", "10", "9", "11"],
["0", "2", "1", "3", "6", "5", "4", "9", "11", "7", "10", "8"]
]
}
}
}
},
"_refs": {
"ee689053-9468-41a5-95bc-8e76ae61bd73": {
"_type": "EmbeddedNumField",
"data": {
"num_field": "3d20d31c-f11f-482f-aaf9-164ff355c054",
"embedding": "00a2c7d1-3560-4dcc-8b75-16ea45bac968"
}
},
"ffe1bae3-b384-44a9-a574-b9c4afd3ec91": {
"_type": "MatSpace",
"data": {"base_ring": "ee689053-9468-41a5-95bc-8e76ae61bd73", "ncols": "3", "nrows": "0"}
},
"0478086e-10f6-4d36-a0f9-354d30b130dd": {
"_type": "MatSpace",
"data": {"base_ring": "ee689053-9468-41a5-95bc-8e76ae61bd73", "ncols": "3", "nrows": "12"}
},
"aaf77b9d-df0a-4e5e-9169-446f9f656271": {
"_type": "MatSpace",
"data": {"base_ring": "ee689053-9468-41a5-95bc-8e76ae61bd73", "ncols": "3", "nrows": "15"}
},
"3d20d31c-f11f-482f-aaf9-164ff355c054": {
"_type": "AbsSimpleNumField",
"data": {
"def_pol": {
"_type": {"name": "PolyRingElem", "params": "d02d8437-061b-403c-993a-5091ee59780c"},
"data": [["0", "-5"], ["2", "1"]]
},
"var": "sqrt(5)"
}
},
"00a2c7d1-3560-4dcc-8b75-16ea45bac968": {
"_type": "Hecke.AbsSimpleNumFieldEmbedding",
"data": {
"num_field": "3d20d31c-f11f-482f-aaf9-164ff355c054",
"data": {
"_type": {"name": "AcbFieldElem", "params": {"_type": "AcbField", "data": "35"}},
"data": ["478dde6e5 -21 20000003 -3e", "0 0 0 0"]
}
}
},
"d02d8437-061b-403c-993a-5091ee59780c": {"_type": "PolyRing", "data": {"base_ring": {"_type": "QQField"}, "symbols": ["x"]}}
}
}Profiles: OSCAR v1.1, OSCAR v1.2
Data file: data.mrdi
{
"_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.2.2"]},
"_type": {"name": "PolyhedralFan", "params": "3dad9c06-0c3e-43e5-aedd-633e1d18cb6c"},
"data": {
"_type": {
"name": "Dict",
"params": {
"key_type": "String",
"FAN_DIM": "Base.Int",
"REGULAR": "Bool",
"LINEALITY_SPACE": {"name": "MatElem", "params": "0a4536d8-e9a3-4097-8974-58c0d9840ad8"},
"_coeff": "EmbeddedNumField",
"FAN_AMBIENT_DIM": "Base.Int",
"_type": "String",
"PSEUDO_REGULAR": "Bool",
"LINEAR_SPAN_NORMALS": {"name": "MatElem", "params": "0a4536d8-e9a3-4097-8974-58c0d9840ad8"},
"MAXIMAL_CONES_FACETS": {"name": "Matrix", "params": "Base.Int"},
"MAXIMAL_CONES": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"MAXIMAL_CONES_LINEAR_SPAN_NORMALS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"RAYS": {"name": "MatElem", "params": "197bd141-7100-4580-8d74-9a46ff4604c7"},
"COMPLETE": "Bool",
"FACET_NORMALS": {"name": "MatElem", "params": "b9570ed2-b34b-432f-a8d5-0a706c0c41ca"},
"GROUP": {
"name": "Dict",
"params": {
"key_type": "String",
"RAYS_ACTION": {
"name": "Dict",
"params": {
"key_type": "String",
"GENERATORS": {"name": "Vector", "params": {"name": "Vector", "params": "Base.Int"}}
}
},
"_description": "String"
}
}
}
},
"data": {
"FAN_DIM": "3",
"REGULAR": "true",
"LINEALITY_SPACE": [],
"_coeff": {
"num_field": "8836e28c-1192-4a31-aa02-84baaf95797d",
"embedding": "5b23804f-4148-4cd1-94e7-7f62264dffbc"
},
"FAN_AMBIENT_DIM": "3",
"_type": "fan::PolyhedralFan<OscarNumber>",
"PSEUDO_REGULAR": "true",
"LINEAR_SPAN_NORMALS": [],
"MAXIMAL_CONES_FACETS": [
["1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "-1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "0", "-1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "0", "0", "-1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0"],
["-1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0"],
["0", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "0", "1", "0", "0", "0"],
["0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0"],
["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "-1", "0", "0"],
["0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "1"],
["0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "0", "0", "0", "0", "-1"],
["0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "0", "0", "1"],
["0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "-1", "-1"],
["0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "0", "0"],
["0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0"],
["0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "-1", "0", "0", "0"],
["1", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "0", "0"],
["0", "0", "0", "1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0"],
["0", "0", "1", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0"],
["0", "1", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"],
["-1", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"]
],
"MAXIMAL_CONES": {
"_type": "common::IncidenceMatrix<NonSymmetric>",
"_ns": {"polymake": ["https://polymake.org", "4.13"]},
"data": [
[0, 1, 2],
[1, 2, 5],
[0, 1, 6],
[1, 5, 7],
[0, 2, 4],
[1, 6, 7],
[2, 5, 9],
[2, 4, 9],
[0, 6, 10],
[0, 4, 10],
[3, 5, 7],
[3, 5, 9],
[6, 7, 8],
[6, 8, 10],
[4, 9, 11],
[3, 7, 8],
[4, 10, 11],
[3, 9, 11],
[8, 10, 11],
[3, 8, 11],
{"cols": 12}
]
},
"MAXIMAL_CONES_LINEAR_SPAN_NORMALS": {
"_type": "common::IncidenceMatrix<NonSymmetric>",
"_ns": {"polymake": ["https://polymake.org", "4.13"]},
"data": [
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
[],
{"cols": 0}
]
},
"RAYS": [
[[["0", "-1"]], [["0", "1//2"], ["1", "-1//2"]], []],
[[], [["0", "-1"]], [["0", "1//2"], ["1", "-1//2"]]],
[[], [["0", "-1"]], [["0", "-1//2"], ["1", "1//2"]]],
[[["0", "1"]], [["0", "-1//2"], ["1", "1//2"]], []],
[[["0", "-1"]], [], [["0", "1//2"], ["1", "1//2"]]],
[[["0", "1"]], [["0", "1//2"], ["1", "-1//2"]], []],
[[["0", "-1"]], [], [["0", "-1//2"], ["1", "-1//2"]]],
[[["0", "1"]], [], [["0", "-1//2"], ["1", "-1//2"]]],
[[], [["0", "1"]], [["0", "1//2"], ["1", "-1//2"]]],
[[["0", "1"]], [], [["0", "1//2"], ["1", "1//2"]]],
[[["0", "-1"]], [["0", "-1//2"], ["1", "1//2"]], []],
[[], [["0", "1"]], [["0", "-1//2"], ["1", "1//2"]]]
],
"COMPLETE": "true",
"FACET_NORMALS": [
[[["0", "3//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1"]], [], []],
[[["0", "3//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-3//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-3//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1//2"], ["1", "1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[], [["0", "-1"]], []],
[[["0", "1//2"], ["1", "1//2"]], [["0", "1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "-1//2"], ["1", "-1//2"]], [["0", "-3//2"], ["1", "-1//2"]], [["0", "1"]]],
[[], [], [["0", "-1"]]]
],
"GROUP": {
"RAYS_ACTION": {
"GENERATORS": [
["5", "1", "2", "10", "9", "0", "7", "6", "8", "4", "3", "11"],
["2", "1", "0", "8", "4", "6", "5", "7", "3", "10", "9", "11"],
["0", "2", "1", "3", "6", "5", "4", "9", "11", "7", "10", "8"]
]
},
"_description": "symmetry group induced by the group of the original polytope\n"
}
}
},
"_refs": {
"3dad9c06-0c3e-43e5-aedd-633e1d18cb6c": {
"_type": "EmbeddedNumField",
"data": {
"num_field": "8836e28c-1192-4a31-aa02-84baaf95797d",
"embedding": "5b23804f-4148-4cd1-94e7-7f62264dffbc"
}
},
"0a4536d8-e9a3-4097-8974-58c0d9840ad8": {
"_type": "MatSpace",
"data": {"base_ring": "3dad9c06-0c3e-43e5-aedd-633e1d18cb6c", "ncols": "3", "nrows": "0"}
},
"197bd141-7100-4580-8d74-9a46ff4604c7": {
"_type": "MatSpace",
"data": {"base_ring": "3dad9c06-0c3e-43e5-aedd-633e1d18cb6c", "ncols": "3", "nrows": "12"}
},
"b9570ed2-b34b-432f-a8d5-0a706c0c41ca": {
"_type": "MatSpace",
"data": {"base_ring": "3dad9c06-0c3e-43e5-aedd-633e1d18cb6c", "ncols": "3", "nrows": "15"}
},
"8836e28c-1192-4a31-aa02-84baaf95797d": {
"_type": "AbsSimpleNumField",
"data": {
"def_pol": {
"_type": {"name": "PolyRingElem", "params": "57d3e2d3-c3d6-4216-8860-3da012b62fed"},
"data": [["0", "-5"], ["2", "1"]]
},
"var": "sqrt(5)"
}
},
"5b23804f-4148-4cd1-94e7-7f62264dffbc": {
"_type": "Hecke.AbsSimpleNumFieldEmbedding",
"data": {
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}This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.
Profiles: OSCAR v1.3
Data file: data.mrdi
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}Profiles: OSCAR v1.4
Data file: data.mrdi
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Data file: data.mrdi
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}This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.
Profiles: OSCAR v1.8
Data file: data.mrdi
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