Example: Dodecahedron dictionary
Profiles: OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8
Store both precise and unprecise dodecahedron polyhedra in a dictionary.
Related Specification
Systems
Oscar.jl
Generate code (generate.jl) [ edit ]
using Oscar
d_hedron = dodecahedron()
facets(d_hedron)
vertices(d_hedron)
f_vector(d_hedron)
lattice_points(d_hedron)
obj = Dict{String, Any}(
"unprecise" => polyhedron(Polymake.common.convert_to{Float64}(Oscar.pm_object(d_hedron))),
"precise" => d_hedron,
)
save("data.mrdi", obj)
Data outputs
Profiles: OSCAR v1.2
Data file: data.mrdi
{
"_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.2.2"]},
"_type": {
"name": "Dict",
"params": {
"key_type": "String",
"precise": {"name": "Polyhedron", "params": "ec0a516e-b0b2-469b-828e-d8b5f3c29b83"},
"unprecise": {"name": "Polyhedron", "params": {"_type": "Floats"}}
}
},
"data": {
"precise": {
"_type": {
"name": "Dict",
"params": {
"key_type": "String",
"TRIANGULATION": {
"name": "Dict",
"params": {
"key_type": "String",
"FACETS": {"name": "Vector", "params": {"name": "Set", "params": "Base.Int"}}
}
},
"N_VERTICES": "Base.Int",
"LINEALITY_SPACE": {"name": "MatElem", "params": "2f09315e-08a5-49d1-9df1-d449920a07be"},
"_coeff": "EmbeddedNumField",
"CONE_AMBIENT_DIM": "Base.Int",
"ESSENTIALLY_GENERIC": "Bool",
"LINEALITY_DIM": "Base.Int",
"BOUNDED": "Bool",
"_type": "String",
"COMBINATORIAL_DIM": "Base.Int",
"POINTED": "Bool",
"VERTICES": {"name": "MatElem", "params": "933947b2-bdc8-43aa-be96-31187633b8ec"},
"HASSE_DIAGRAM": {
"name": "Dict",
"params": {
"key_type": "String",
"FACES": {"name": "Vector", "params": {"name": "Set", "params": "Base.Int"}},
"ADJACENCY": "Graph{Directed}",
"BOTTOM_NODE": "Base.Int",
"DECORATION": {
"name": "Vector",
"params": {"name": "Tuple", "params": [{"name": "Set", "params": "Base.Int"}, "Base.Int"]}
},
"TOP_NODE": "Base.Int"
}
},
"AFFINE_HULL": {"name": "MatElem", "params": "2f09315e-08a5-49d1-9df1-d449920a07be"},
"CONE_DIM": "Base.Int",
"DUAL_GRAPH": {"name": "Dict", "params": {"key_type": "String", "ADJACENCY": "Graph{Undirected}"}},
"VERTICES_IN_FACETS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"CENTERED": "Bool",
"FEASIBLE": "Bool",
"FAR_FACE": {"name": "Set", "params": "Base.Int"},
"LATTICE_POINTS_GENERATORS": {
"name": "Tuple",
"params": [
{"name": "MatElem", "params": "e523291a-570b-402b-bf6f-7ac5813eb6f5"},
{"name": "MatElem", "params": "f51d9d2e-a137-4930-9cd9-cf50fcd5e4e3"},
{"name": "MatElem", "params": "f51d9d2e-a137-4930-9cd9-cf50fcd5e4e3"}
]
},
"FACETS": {"name": "MatElem", "params": "63377969-1006-4668-a473-ef0df6d4ed52"},
"GROUP": {
"name": "Dict",
"params": {
"key_type": "String",
"VERTICES_ACTION": {
"name": "Dict",
"params": {
"key_type": "String",
"GENERATORS": {"name": "Vector", "params": {"name": "Vector", "params": "Base.Int"}}
}
}
}
}
}
},
"data": {
"TRIANGULATION": {
"FACETS": [
["0", "4", "2", "1"],
["4", "2", "3", "1"],
["5", "4", "2", "3"],
["5", "4", "6", "3"],
["4", "6", "3", "1"],
["5", "4", "6", "7"],
["5", "4", "2", "8"],
["5", "4", "7", "8"],
["4", "7", "9", "8"],
["5", "6", "10", "3"],
["5", "6", "7", "10"],
["5", "7", "10", "8"],
["7", "10", "9", "8"],
["7", "11", "10", "9"],
["6", "7", "11", "10"],
["10", "9", "12", "8"],
["11", "10", "9", "12"],
["5", "10", "12", "8"],
["13", "9", "12", "8"],
["13", "11", "9", "12"],
["7", "11", "9", "14"],
["13", "11", "9", "14"],
["15", "11", "10", "12"],
["13", "15", "11", "12"],
["13", "15", "11", "14"],
["13", "15", "16", "14"],
["13", "16", "9", "14"],
["15", "16", "14", "17"],
["15", "11", "14", "17"],
["13", "15", "16", "18"],
["15", "16", "18", "17"],
["15", "18", "17", "19"]
]
},
"N_VERTICES": "20",
"LINEALITY_SPACE": [],
"_coeff": {
"num_field": "8836e28c-1192-4a31-aa02-84baaf95797d",
"embedding": "5b23804f-4148-4cd1-94e7-7f62264dffbc"
},
"CONE_AMBIENT_DIM": "4",
"ESSENTIALLY_GENERIC": "false",
"LINEALITY_DIM": "0",
"BOUNDED": "true",
"_type": "polytope::Polytope<OscarNumber>",
"COMBINATORIAL_DIM": "3",
"POINTED": "true",
"VERTICES": [
[[["0", "1"]], [["0", "1//2"]], [["0", "3//4"], ["1", "1//4"]], []],
[[["0", "1"]], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]], []],
[
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[["0", "1//4"], ["1", "1//4"]]
],
[
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[["0", "1//4"], ["1", "1//4"]],
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],
[
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[["0", "1//4"], ["1", "1//4"]],
[["0", "1//4"], ["1", "1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "3//4"], ["1", "1//4"]]],
[
[["0", "1"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "1//4"], ["1", "1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
[[["0", "1"]], [["0", "3//4"], ["1", "1//4"]], [], [["0", "1//2"]]],
[[["0", "1"]], [["0", "3//4"], ["1", "1//4"]], [], [["0", "-1//2"]]],
[[["0", "1"]], [["0", "-3//4"], ["1", "-1//4"]], [], [["0", "1//2"]]],
[[["0", "1"]], [["0", "-3//4"], ["1", "-1//4"]], [], [["0", "-1//2"]]],
[[["0", "1"]], [], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]]],
[
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[["0", "-1//4"], ["1", "-1//4"]],
[["0", "1//4"], ["1", "1//4"]]
],
[[["0", "1"]], [], [["0", "-1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
[
[["0", "1"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "1//4"], ["1", "1//4"]]
],
[
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[["0", "1//4"], ["1", "1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[
[["0", "1"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [["0", "1//2"]], [["0", "-3//4"], ["1", "-1//4"]], []],
[[["0", "1"]], [["0", "-1//2"]], [["0", "-3//4"], ["1", "-1//4"]], []]
],
"HASSE_DIAGRAM": {
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"7",
"12",
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"17",
"1",
"19",
"0",
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],
["0", "4", "2", "9", "8"],
["0", "5", "2", "3", "1"],
["0", "4", "6", "7", "1"],
["15", "11", "10", "17", "19"],
["4", "16", "7", "9", "14"],
["6", "11", "10", "3", "1"],
["5", "13", "2", "12", "8"],
["5", "15", "10", "12", "3"],
["13", "15", "18", "12", "19"],
["6", "7", "11", "14", "17"],
["13", "16", "18", "9", "8"],
["16", "18", "14", "17", "19"],
["0", "2"],
["0", "4"],
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["2", "8"],
["9", "8"],
["0", "1"],
["3", "1"],
["5", "2"],
["5", "3"],
["4", "7"],
["6", "1"],
["6", "7"],
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["11", "17"],
["17", "19"],
["7", "14"],
["16", "9"],
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["5", "12"],
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["14", "17"],
["16", "18"],
["0"],
["1"],
["2"],
["3"],
["4"],
["5"],
["6"],
["7"],
["8"],
["9"],
["10"],
["11"],
["12"],
["13"],
["14"],
["15"],
["16"],
["17"],
["18"],
["19"],
[]
],
"ADJACENCY": {
"data": [
[],
[0],
[0],
[0],
[0],
[0],
[0],
[0],
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[18, 19, 23],
[13, 16, 20],
[19, 21, 33],
[14, 15, 22],
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[25, 28, 34],
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[43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62]
],
"_ns": {"polymake": ["https://polymake.org", "4.13"]},
"_type": "common::GraphAdjacency<Directed>"
},
"BOTTOM_NODE": "63",
"DECORATION": [
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],
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],
[["0", "4", "2", "9", "8"], "3"],
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[["0", "4", "6", "7", "1"], "3"],
[["15", "11", "10", "17", "19"], "3"],
[["4", "16", "7", "9", "14"], "3"],
[["6", "11", "10", "3", "1"], "3"],
[["5", "13", "2", "12", "8"], "3"],
[["5", "15", "10", "12", "3"], "3"],
[["13", "15", "18", "12", "19"], "3"],
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[["15", "19"], "2"],
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[["7", "14"], "2"],
[["16", "9"], "2"],
[["16", "14"], "2"],
[["10", "3"], "2"],
[["6", "11"], "2"],
[["5", "12"], "2"],
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[["13", "8"], "2"],
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[["13", "18"], "2"],
[["18", "19"], "2"],
[["14", "17"], "2"],
[["16", "18"], "2"],
[["0"], "1"],
[["1"], "1"],
[["2"], "1"],
[["3"], "1"],
[["4"], "1"],
[["5"], "1"],
[["6"], "1"],
[["7"], "1"],
[["8"], "1"],
[["9"], "1"],
[["10"], "1"],
[["11"], "1"],
[["12"], "1"],
[["13"], "1"],
[["14"], "1"],
[["15"], "1"],
[["16"], "1"],
[["17"], "1"],
[["18"], "1"],
[["19"], "1"],
[[], "0"]
],
"TOP_NODE": "0"
},
"AFFINE_HULL": [],
"CONE_DIM": "4",
"DUAL_GRAPH": {
"ADJACENCY": {
"data": [
[1, 2, 4, 6, 10],
[0, 2, 5, 6, 7],
[0, 1, 4, 5, 9],
[5, 7, 8, 9, 11],
[0, 2, 9, 10, 11],
[1, 2, 3, 7, 9],
[0, 1, 7, 8, 10],
[1, 3, 5, 6, 8],
[3, 6, 7, 10, 11],
[2, 3, 4, 5, 11],
[0, 4, 6, 8, 11],
[3, 4, 8, 9, 10]
],
"_ns": {"polymake": ["https://polymake.org", "4.13"]},
"_type": "common::GraphAdjacency<Undirected>"
}
},
"VERTICES_IN_FACETS": {
"data": [
[0, 2, 4, 8, 9],
[0, 1, 2, 3, 5],
[0, 1, 4, 6, 7],
[10, 11, 15, 17, 19],
[4, 7, 9, 14, 16],
[1, 3, 6, 10, 11],
[2, 5, 8, 12, 13],
[3, 5, 10, 12, 15],
[12, 13, 15, 18, 19],
[6, 7, 11, 14, 17],
[8, 9, 13, 16, 18],
[14, 16, 17, 18, 19],
{"cols": 20}
],
"_type": "common::IncidenceMatrix<NonSymmetric>",
"_ns": {"polymake": ["https://polymake.org", "4.13"]}
},
"CENTERED": "true",
"FEASIBLE": "true",
"FAR_FACE": [],
"LATTICE_POINTS_GENERATORS": [
[
["1", "-1", "0", "0"],
["1", "0", "-1", "0"],
["1", "0", "0", "-1"],
["1", "0", "0", "0"],
["1", "0", "0", "1"],
["1", "0", "1", "0"],
["1", "1", "0", "0"]
],
[],
[]
],
"FACETS": [
[[["0", "1"], ["1", "1//2"]], [["0", "-1//2"], ["1", "-1//2"]], [["0", "-1"]], []],
[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]], []],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]]]
],
"GROUP": {
"VERTICES_ACTION": {
"GENERATORS": [
[
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"0",
"3",
"2",
"6",
"5",
"4",
"7",
"10",
"11",
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],
[
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],
[
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"10",
"14",
"16",
"12",
"17",
"13",
"15",
"18",
"19"
]
]
}
}
}
},
"unprecise": {
"AFFINE_HULL": [{"cols": 4}],
"FAR_FACE": [],
"COMBINATORIAL_DIM": 3,
"GROUP": [
{
"VERTICES_ACTION": {
"GENERATORS": [
[1, 0, 3, 2, 6, 5, 4, 7, 10, 11, 8, 9, 12, 15, 14, 13, 17, 16, 19, 18],
[0, 2, 1, 5, 4, 3, 8, 9, 6, 7, 12, 13, 10, 11, 16, 15, 14, 18, 17, 19],
[0, 1, 4, 6, 2, 7, 3, 5, 9, 8, 11, 10, 14, 16, 12, 17, 13, 15, 18, 19]
]
}
}
],
"TRIANGULATION": [
{
"FACETS": [
[0, 1, 2, 4],
[1, 2, 3, 4],
[2, 3, 4, 5],
[3, 4, 5, 6],
[1, 3, 4, 6],
[4, 5, 6, 7],
[2, 4, 5, 8],
[4, 5, 7, 8],
[4, 7, 8, 9],
[3, 5, 6, 10],
[5, 6, 7, 10],
[5, 7, 8, 10],
[7, 8, 9, 10],
[7, 9, 10, 11],
[6, 7, 10, 11],
[8, 9, 10, 12],
[9, 10, 11, 12],
[5, 8, 10, 12],
[8, 9, 12, 13],
[9, 11, 12, 13],
[7, 9, 11, 14],
[9, 11, 13, 14],
[10, 11, 12, 15],
[11, 12, 13, 15],
[11, 13, 14, 15],
[13, 14, 15, 16],
[9, 13, 14, 16],
[14, 15, 16, 17],
[11, 14, 15, 17],
[13, 15, 16, 18],
[15, 16, 17, 18],
[15, 17, 18, 19]
]
}
],
"VERTICES": [
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{"0": 1, "1": -0.5, "2": 1.30901699431706},
[1, 0.809016994346166, 0.809016994346166, 0.809016994346166],
[1, -0.809016994346166, 0.809016994346166, 0.809016994346166],
[1, 0.809016994346166, 0.809016994346166, -0.809016994346166],
{"0": 1, "2": 0.5, "3": 1.30901699431706},
[1, -0.809016994346166, 0.809016994346166, -0.809016994346166],
{"0": 1, "2": 0.5, "3": -1.30901699431706},
{"0": 1, "1": 1.30901699431706, "3": 0.5},
{"0": 1, "1": 1.30901699431706, "3": -0.5},
{"0": 1, "1": -1.30901699431706, "3": 0.5},
{"0": 1, "1": -1.30901699431706, "3": -0.5},
{"0": 1, "2": -0.5, "3": 1.30901699431706},
[1, 0.809016994346166, -0.809016994346166, 0.809016994346166],
{"0": 1, "2": -0.5, "3": -1.30901699431706},
[1, -0.809016994346166, -0.809016994346166, 0.809016994346166],
[1, 0.809016994346166, -0.809016994346166, -0.809016994346166],
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{"0": 1, "1": 0.5, "2": -1.30901699431706},
{"0": 1, "1": -0.5, "2": -1.30901699431706},
{"cols": 4}
],
"_ns": {"polymake": ["https://polymake.org", "4.13"]},
"DUAL_GRAPH": {
"ADJACENCY": [
[1, 2, 4, 6, 10],
[0, 2, 5, 6, 7],
[0, 1, 4, 5, 9],
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}Profiles: OSCAR v1.4
Data file: data.mrdi
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}Profiles: OSCAR v1.5, OSCAR v1.6, OSCAR v1.7
Data file: data.mrdi
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Profiles: OSCAR v1.8
Data file: data.mrdi
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