{
  "vercy": "1.0-draft",
  "publication": {
    "status": "research-draft",
    "adjudicationStatus": "unreviewed",
    "publishableCanonical": false,
    "generatedAt": "2026-09-13T15:18:08Z",
    "providers": [
      "Claude"
    ],
    "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify",
    "pass": 2,
    "wave": 4,
    "engine": "claude",
    "enrichment": {
      "pass": 3,
      "engine": "claude",
      "producedAt": "2026-10-06T11:00:00Z",
      "ingestedAt": "2026-10-06T07:36:56+00:00",
      "fields": [
        "agent_conduct",
        "ethics",
        "owners"
      ]
    },
    "revisions": [
      {
        "at": "2026-10-06T22:46:52+00:00",
        "engine": "codex",
        "fields": [
          "definition"
        ],
        "answering_review": "18fb6dbeb14fb8ea2e1ab4a041c8be25ff2455705807cbfce8155e8bae56f936"
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    "gate": {
      "passed": true,
      "version": "1.0",
      "at": "2026-10-07T10:10:29+00:00",
      "evidence": [
        "completeness 1.00",
        "sense: Wikidata description",
        "2 live sources",
        "review by codex: pass"
      ]
    }
  },
  "metaModel": {
    "id": "THING-Q2745944",
    "registryId": "vr.tr.regular-polytope",
    "name": "regular polytope",
    "version": "0.2.0-wave.4",
    "entryKind": "thing",
    "family": "Thing Registry",
    "domain": [
      "XCT.QLT"
    ],
    "status": "research-draft"
  },
  "canonicalUrl": "https://ver.cy/models/thing/q2745944/",
  "model": {
    "registry_id": "vr.tr.regular-polytope",
    "name": "regular polytope",
    "purpose": "Let an agent explain regular polytopes and their classification, relay the enumeration in each dimension and the extension to honeycombs and abstract polytopes from geometry sources, describe the hyperbolic honeycombs the registry aliases name, and distinguish regular polytopes from uniform and semiregular polytopes and from regular polygons and polyhedra alone.",
    "definition": "A polytope whose symmetry group acts transitively on its flags, so that all its faces, edges and vertices of each kind are alike, generalising the regular polygons and the five Platonic solids to higher dimensions, with six convex regular 4-polytopes such as the 120-cell and three convex regular polytopes in each dimension five and above, extended to regular tessellations and honeycombs of Euclidean and hyperbolic space, such as the order-5 5-cell honeycomb, the 120-cell honeycomb and the order-7, order-8 and order-9 tetrahedral honeycombs, and to abstract regular polytopes including degenerate cases such as the edgeless map.",
    "what_it_is_for": "Not applicable; a mathematical object.",
    "affordances": [
      "explain the concept",
      "relay classification",
      "describe honeycombs",
      "distinguish related objects"
    ],
    "distinguishing_features": [
      "Flag transitivity",
      "Complete classification",
      "Schlafli symbols",
      "Extension to honeycombs"
    ],
    "appearance": "Not a visible object; highly symmetric figures such as the Platonic solids.",
    "visual_identification": [
      "Flag-transitive polytope",
      "Platonic solids, 120-cell, regular honeycombs such as order-8 tetrahedral, edgeless map",
      "Uniform polytopes are vertex-transitive only; semiregular have several face types; polygons and polyhedra are dimensions two and three"
    ],
    "physical_properties": [
      {
        "quantity": "regular polyhedra",
        "typical_range": "5",
        "unit": "count",
        "note": "Platonic solids"
      },
      {
        "quantity": "regular 4-polytopes",
        "typical_range": "6",
        "unit": "count",
        "note": ""
      },
      {
        "quantity": "regular polytopes, dimension 5 and above",
        "typical_range": "3",
        "unit": "count",
        "note": "per dimension"
      },
      {
        "quantity": "Schlafli symbol",
        "typical_range": "notation for regular polytopes",
        "unit": "note",
        "note": ""
      }
    ],
    "families_and_kinds": [
      "regular polygons",
      "Platonic solids and Kepler-Poinsot polyhedra",
      "regular 4-polytopes such as the 120-cell",
      "simplex, hypercube and cross-polytope families",
      "regular Euclidean and hyperbolic honeycombs",
      "abstract regular polytopes including the edgeless map"
    ],
    "related_models": [
      {
        "relation": "is a kind of",
        "target": "polytope",
        "why": "in registry terms"
      },
      {
        "relation": "is a kind of",
        "target": "symmetrical object",
        "why": "in registry terms"
      },
      {
        "relation": "is classified by",
        "target": "Schlafli symbol",
        "why": "in each dimension"
      },
      {
        "relation": "was systematised by",
        "target": "H. S. M. Coxeter",
        "why": "in Regular Polytopes"
      }
    ],
    "identifiers": [],
    "standards_and_regulation": [
      "No regulation"
    ],
    "failure_modes_and_hazards": [
      "Confusing regular with uniform polytopes",
      "Registry aliases naming specific hyperbolic honeycombs",
      "Misreading Schlafli symbols"
    ],
    "in_scope": [],
    "out_of_scope": [],
    "characteristics": [],
    "agent_conduct": {
      "may": [
        "State the definition of a regular polytope and list known families with their properties.",
        "Compute or check symmetry and face counts for a stated polytope."
      ],
      "must_not": [
        "Claim a polytope is regular without checking flag transitivity.",
        "Attribute discoveries to the wrong mathematicians.",
        "Present conjecture as proven classification."
      ],
      "requires_human": [
        "Publishing a new classification result."
      ]
    },
    "ethics": {
      "considerations": [
        "Credit for classification belongs to those who proved it.",
        "Errors in geometry teaching spread widely through students."
      ],
      "affected_parties": [
        "Students",
        "Researchers",
        "Readers"
      ]
    },
    "owners": {
      "steward": "Nobody owns the concept; the mathematical community maintains it through peer review.",
      "master_systems": []
    }
  },
  "sources": [
    {
      "id": "wikidata",
      "title": "Wikidata item Q2745944: regular polytope",
      "url": "https://www.wikidata.org/wiki/Q2745944",
      "url_status": "live",
      "what_it_supports": "identity and sense of the item",
      "checked_by": "wikidata-api"
    },
    {
      "id": "wikipedia-en",
      "title": "Wikipedia: Regular polytope",
      "url": "https://en.wikipedia.org/wiki/Regular_polytope",
      "url_status": "live",
      "what_it_supports": "general description of the item",
      "checked_by": "wikidata-api sitelink"
    }
  ],
  "structure": {
    "bundles": [
      {
        "id": "understand",
        "name": "Understand",
        "description": "What a regular polytope is.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "definition",
            "name": "Definition",
            "description": "Definition.",
            "findings": [
              {
                "id": "definition-finding",
                "name": "Definition",
                "description": "Definition.",
                "questions": [
                  {
                    "text": "What is a regular polytope, and how does it differ from uniform and semiregular polytopes and from regular polygons and polyhedra?",
                    "kind": "definition"
                  },
                  {
                    "text": "Is the question about a dimension, a specific polytope, a honeycomb or abstract theory?",
                    "kind": "boundary"
                  }
                ]
              }
            ]
          },
          {
            "id": "examples",
            "name": "Examples",
            "description": "Examples.",
            "findings": [
              {
                "id": "examples-finding",
                "name": "Examples",
                "description": "Examples.",
                "questions": [
                  {
                    "text": "What are the 120-cell, the regular honeycombs such as the order-8 tetrahedral honeycomb and the edgeless map?",
                    "kind": "definition"
                  },
                  {
                    "text": "Which entry fits the specific object?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "classification",
        "name": "Classification",
        "description": "Classification.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "dimensions",
            "name": "Dimensions",
            "description": "By dimension.",
            "findings": [
              {
                "id": "dimensions-finding",
                "name": "Dimensions",
                "description": "Dimensions.",
                "questions": [
                  {
                    "text": "How are regular polytopes enumerated in each dimension, and why only three from dimension five?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which references are standard?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          },
          {
            "id": "honeycombs",
            "name": "Honeycombs",
            "description": "Honeycombs.",
            "findings": [
              {
                "id": "honeycombs-finding",
                "name": "Honeycombs",
                "description": "Honeycombs.",
                "questions": [
                  {
                    "text": "How are regular tessellations and honeycombs classified in Euclidean and hyperbolic spaces?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which sources are cited?",
                    "kind": "provenance"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "theory",
        "name": "Theory",
        "description": "Theory.",
        "rationale": "Science.",
        "layers": [
          {
            "id": "symmetry",
            "name": "Symmetry",
            "description": "Symmetry groups.",
            "findings": [
              {
                "id": "symmetry-finding",
                "name": "Symmetry",
                "description": "Symmetry.",
                "questions": [
                  {
                    "text": "How do Coxeter groups and Schlafli symbols describe regular polytopes?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits Coxeter group?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "abstract",
            "name": "Abstract",
            "description": "Abstract polytopes.",
            "findings": [
              {
                "id": "abstract-finding",
                "name": "Abstract",
                "description": "Abstract.",
                "questions": [
                  {
                    "text": "What are abstract regular polytopes and degenerate cases such as the edgeless map?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits abstract polytope?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      },
      {
        "id": "context",
        "name": "Context",
        "description": "History and applications.",
        "rationale": "Context.",
        "layers": [
          {
            "id": "history",
            "name": "History",
            "description": "History.",
            "findings": [
              {
                "id": "history-finding",
                "name": "History",
                "description": "History.",
                "questions": [
                  {
                    "text": "How did Schlafli, Coxeter and others develop the theory?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits the history of geometry?",
                    "kind": "action"
                  }
                ]
              }
            ]
          },
          {
            "id": "applications",
            "name": "Applications",
            "description": "Applications.",
            "findings": [
              {
                "id": "applications-finding",
                "name": "Applications",
                "description": "Applications.",
                "questions": [
                  {
                    "text": "Where do regular polytopes appear in crystallography, physics and art?",
                    "kind": "provenance"
                  },
                  {
                    "text": "Which entry fits polytope visualisation?",
                    "kind": "action"
                  }
                ]
              }
            ]
          }
        ]
      }
    ]
  },
  "openQuestions": [
    "Should regular honeycomb and abstract polytope be separate primary entries?",
    "How should geometry sources be linked?",
    "The registry entry has merged aliases naming specific honeycombs and a degenerate map; should they be split off?"
  ],
  "statistics": {
    "bundles": 4,
    "layers": 8,
    "findings": 8,
    "questions": 16
  }
}