Specification: Polyhedral Fans

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

PolyhedralFan is currently documented in the OSCAR v1.7 profile through the rosetta-stone corpus. This page records the present encoding shape and should be read as a profile-specific type description.

Encoding Notes

• Set _type to "PolyhedralFan" when this type appears at the root of a serialized object.
• Interpret the payload under data according to the active namespace and profile version.
• Follow the linked examples for the currently documented payload shape and referenced ambient objects.

Canonical Example Payload

The following payload is taken directly from the current rosetta-stone corpus.

{
  "_ns": {
    "Oscar": [
      "https://github.com/oscar-system/Oscar.jl",
      "1.8.0-DEV-1-8dea7e5a4d0cdef038b2fa2cd018d08201b4ac07"
    ]
  },
  "_type": {
    "name": "PolyhedralFan",
    "params": {
      "field": "1ac3a9bc-16d8-41e9-8e50-1f15699f8342",
      "pm_params": {
        "name": "Dict",
        "params": {
          "key_params": "Symbol",
          "_polymake_type": "String",
          "GROUP": {
            "name": "Tuple",
            "params": [
              {
                "name": "Dict",
                "params": {
                  "key_params": "Symbol",
                  "_description": "String",
                  "RAYS_ACTION.GENERATORS": {"name": "Vector", "params": {"name": "Vector", "params": "Base.Int"}}
                }
              }
            ]
          },
          "PSEUDO_REGULAR": "Bool",
          "MAXIMAL_CONES_FACETS": {"name": "Matrix", "params": "Base.Int"},
          "REGULAR": "Bool",
          "RAYS": {"name": "MatElem", "params": "37c9fc4b-6343-4b74-bdf8-430271aa0993"},
          "LINEAR_SPAN_NORMALS": {"name": "MatElem", "params": "b7924452-ed74-43cb-bd73-5dd29c534c8f"},
          "MAXIMAL_CONES_LINEAR_SPAN_NORMALS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
          "COMPLETE": "Bool",
          "FACET_NORMALS": {"name": "MatElem", "params": "7010bb0f-3b8b-490f-a506-a6f4f59675d3"},
          "LINEALITY_SPACE": {"name": "MatElem", "params": "b7924452-ed74-43cb-bd73-5dd29c534c8f"},
          "FAN_DIM": "Base.Int",
          "MAXIMAL_CONES": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
          "FAN_AMBIENT_DIM": "Base.Int"
        }
      }
    }
  },
  "data": {
    "_polymake_type": "fan::PolyhedralFan<OscarNumber>",
    "GROUP": [
      {
        "_description": "symmetry group induced by the group of the original polytope\n",
        "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"]
        ]
      }
    ],
    "PSEUDO_REGULAR": true,
    "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"]
    ],
    "REGULAR": true,
    "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"]]]
    ],
    "LINEAR_SPAN_NORMALS": [],
    "MAXIMAL_CONES_LINEAR_SPAN_NORMALS": {
      "_type": "common::IncidenceMatrix<NonSymmetric>",
      "data": [[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], {"cols": 0}],
      "_ns": {"polymake": ["https://polymake.org", "4.15"]}
    },
    "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"]]]
    ],
    "LINEALITY_SPACE": [],
    "FAN_DIM": "3",
    "MAXIMAL_CONES": {
      "_ns": {"polymake": ["https://polymake.org", "4.15"]},
      "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>"
    },
    "FAN_AMBIENT_DIM": "3"
  },
  "_refs": {
    "1ac3a9bc-16d8-41e9-8e50-1f15699f8342": {
      "_type": {"name": "EmbeddedNumField", "params": "a07ce4fe-c7a5-47ce-93aa-ec518fc0cac9"},
      "data": []
    },
    "37c9fc4b-6343-4b74-bdf8-430271aa0993": {
      "_type": {"name": "MatSpace", "params": "1ac3a9bc-16d8-41e9-8e50-1f15699f8342"},
      "data": {"ncols": "3", "nrows": "12"}
    },
    "b7924452-ed74-43cb-bd73-5dd29c534c8f": {
      "_type": {"name": "MatSpace", "params": "1ac3a9bc-16d8-41e9-8e50-1f15699f8342"},
      "data": {"ncols": "3", "nrows": "0"}
    },
    "7010bb0f-3b8b-490f-a506-a6f4f59675d3": {
      "_type": {"name": "MatSpace", "params": "1ac3a9bc-16d8-41e9-8e50-1f15699f8342"},
      "data": {"ncols": "3", "nrows": "15"}
    },
    "a07ce4fe-c7a5-47ce-93aa-ec518fc0cac9": {
      "_type": {"name": "Hecke.AbsSimpleNumFieldEmbedding", "params": "371cfcb2-1d38-46f6-9253-e148756b3bd4"},
      "data": ["478dde6e5 -21 10000001 -3d", "0 0 0 0"]
    },
    "371cfcb2-1d38-46f6-9253-e148756b3bd4": {
      "_type": {"name": "AbsSimpleNumField", "params": "60404de9-8db1-4fbc-93e4-be75077f781e"},
      "data": {"def_pol": [["0", "-5"], ["2", "1"]], "var": "sqrt(5)"}
    },
    "60404de9-8db1-4fbc-93e4-be75077f781e": {"_type": {"name": "PolyRing", "params": {"_type": "QQField"}}, "data": {"symbols": ["x"]}}
  }
}

Documented Profiles in This Corpus

This table records the profile/version pairs currently represented by the rosetta-stone examples for this data type. Add new rows as new systems or encoding revisions are documented.

Rosetta Stone Examples

• Normal fan of dodecahedron
• Normal fan of square