{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-12T09:17:06Z", "providers": [ "Codex" ], "breadth": "recalled by Codex without web access - no source was read", "missingProviders": [], "pass": 2, "cost": { "grok": { "seconds": 20.5, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a094e6-e33f-7d60-971b-234f41028289\n--------\nuser\nDescribe what is already known about one registered thing. Answer as JSON only, no prose around it.\n\nThing: dodecadodecahedron\nSense to describe: (none recorded)\nDomain code: XCT.QLT\nAlso known as: (none)\n\n\nContext for this batch of 1001 things:\n# Batch 043: 1", "usd": 0.0, "recall": true }, "codex": { "seconds": 72.7, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.4\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a094e6-e33c-7b70-8746-868418ee9ba9\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: dodecadodecahedron\nRegistry id: vr.tr.dodecadodecahedron\nPlane / domain: XCT / XCT.QLT\nRegistry definition: (none recorded)\nNames folded into this en" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T12:00:00Z", "ingestedAt": "2026-10-06T08:41:16+00:00", "fields": [ "agent_conduct", "ethics", "failure_modes_and_hazards", "owners", "visual_identification" ] }, "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-Q3033696", "registryId": "vr.tr.dodecadodecahedron", "name": "dodecadodecahedron", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q3033696/", "model": { "registry_id": "vr.tr.dodecadodecahedron", "name": "dodecadodecahedron", "purpose": "Enable an agent to recognise a dodecadodecahedron, validate its geometric representation, and choose operations that preserve or explicitly transform its identity.", "definition": "The dodecadodecahedron is a nonconvex uniform polyhedron with 12 regular pentagonal faces and 12 regular pentagrammic faces, meeting alternately four at each of its 30 equivalent vertices.", "scope_statement": "This model owns the mathematical identity and representation requirements of vr.tr.dodecadodecahedron in XCT / XCT.QLT, including face incidence, star-face interpretation, geometric validation, and relationships to neighbouring polyhedra.", "in_scope": [ "Recognition through pentagonal and pentagrammic faces and their incidence", "Distinction between mathematical edges and incidental geometric intersections", "Validation of regular faces, equal edges, and vertex transitivity", "Coordinate, face-cycle, and rendered representations of the same polyhedron", "Construction and transformation relationships that establish or change identity" ], "out_of_scope": [ "The general classification of all uniform polyhedra", "Independent models of the great dodecahedron and small stellated dodecahedron", "Independent models of snub, truncated, and ditrigonal dodecadodecahedra", "Material strength, fabrication tolerances, and manufacturing processes for physical replicas", "General mesh-processing algorithms unrelated to preserving this polyhedron's incidence" ], "distinguishing_features": [ "The face inventory is 12 regular pentagons and 12 regular pentagrams, with 30 vertices and 60 edges. [Robert Webb's model](https://software3d.com/Dodecadodeca.php)", "The cyclic face sequence at each vertex alternates pentagram, pentagon, pentagram, pentagon; face counts alone are insufficient for recognition. [Robert Webb's model](https://software3d.com/Dodecadodeca.php)", "Pentagram crossings and intersections between faces must not automatically become additional polyhedral vertices or edges. [Robert Webb's topological representation](https://software3d.com/Dodecadodeca.php)", "A candidate must satisfy uniformity through regular faces and symmetry-equivalent vertices; a star-shaped silhouette or a compound of dodecahedra does not establish identity." ], "characteristics": [ { "name": "Face inventory", "kind": "category", "unit_or_values": "12 pentagons {5} and 12 pentagrams {5/2}", "why_it_matters": "Provides the first structural recognition test." }, { "name": "Incidence counts", "kind": "measurement", "unit_or_values": "30 vertices; 60 edges; 24 faces", "why_it_matters": "Detects missing faces and accidental subdivision at crossings." }, { "name": "Cyclic vertex configuration", "kind": "category", "unit_or_values": "5/2.5.5/2.5, up to cyclic rotation and reversal", "why_it_matters": "Tests how the two face types meet." }, { "name": "Edge scale", "kind": "measurement", "unit_or_values": "Positive edge length a; dimensionless normalization or declared length unit", "why_it_matters": "Separates geometric identity from size and permits comparable measurements." }, { "name": "Regularity residual", "kind": "measurement", "unit_or_values": "Maximum relative edge-length deviation and face-planarity residual divided by a", "why_it_matters": "Distinguishes exact realizations from numerical approximations." }, { "name": "Representation validity", "kind": "state", "unit_or_values": "Unverified; incidence-validated; geometry-validated; rejected", "why_it_matters": "Determines whether recognition, measurement, or export is justified." }, { "name": "Face-interior interpretation", "kind": "category", "unit_or_values": "Boundary-only; even-odd fill; winding-based fill; explicitly specified alternative", "why_it_matters": "Makes rendering and area or volume calculations interpretable." } ], "affordances": [ "Validate a candidate using face cycles, incidence counts, regularity, and symmetry", "Generate or compare coordinate realizations under rigid motion and uniform scaling", "Render pentagonal and pentagrammic face families separately to expose their incidence", "Compute geometric quantities after declaring normalization and intersection conventions", "Construct related polyhedra while recording when the result leaves this registry identity", "Export a visual or fabrication representation with mathematical faces mapped to output pieces" ], "agent_conduct": { "may": [ "Explain the dodecadodecahedron's faces, vertex figure and relation to other uniform polyhedra.", "Generate accurate models or images of it from verified coordinates." ], "must_not": [ "Present an incorrect model or wrong face counts as accurate.", "Confuse it with similarly named star polyhedra in teaching material.", "Copy published images or models without credit." ], "requires_human": [ "Publishing new claims about its properties under a person's name." ] }, "ethics": { "considerations": [ "Accuracy and credit matter in mathematical teaching and publication." ], "affected_parties": [ "Students", "Mathematicians", "Model makers" ] }, "owners": { "steward": "Nobody owns it; it is a concept of geometry.", "master_systems": [] }, "visual_identification": [ "Twelve pentagons and twelve pentagrams crossing through each other, four faces at each vertex." ], "failure_modes_and_hazards": [ "Self-intersecting faces are easily mis-rendered by software." ], "what_it_is_for": [ "The dodecadodecahedron is encountered in the study of uniform polyhedra, symmetry and nonconvex geometry.", "Mathematical models and computer graphics use it to explore intersecting faces and the distinction between geometric surfaces and solid boundaries.", "Validating a representation requires preserving its pentagonal and pentagrammic faces and their incidence relationships." ], "facets_not_applicable": { "interfaces": "No specific standard, law or official classification applies to this abstract polyhedron as such." } }, "sources": [ { "id": "wikidata", "title": "Wikidata item Q3033696: dodecadodecahedron", "url": "https://www.wikidata.org/wiki/Q3033696", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" }, { "id": "wikipedia-en", "title": "Wikipedia: Dodecadodecahedron", "url": "https://en.wikipedia.org/wiki/Dodecadodecahedron", "url_status": "live", "what_it_supports": "general description of the item", "checked_by": "wikidata-api sitelink" } ], "structure": { "bundles": [ { "id": "identity-and-recognition", "name": "Identity and recognition", "description": "Establish whether a named or supplied object represents the registered dodecadodecahedron.", "rationale": "Similar names and star-shaped images can conceal different incidence structures.", "layers": [ { "id": "name-resolution", "name": "Name resolution", "description": "Resolve names and catalogue references without creating additional registry things.", "findings": [ { "id": "catalogue-identity", "name": "Catalogue identity", "description": "Require catalogue names, numbering conventions, and geometric evidence to agree.", "questions": [ { "text": "Which source and numbering system identify the candidate as the dodecadodecahedron?", "kind": "provenance", "id": "catalogue-identity-q01" }, { "text": "Does a qualified name denote this same object or a snub, truncated, or ditrigonal neighbour?", "kind": "boundary", "id": "catalogue-identity-q02" } ] } ] }, { "id": "structural-recognition", "name": "Structural recognition", "description": "Apply the face and vertex tests that establish the intended polyhedron.", "findings": [ { "id": "alternating-face-test", "name": "Alternating face test", "description": "Check the two face families and their alternating cyclic arrangement at every vertex.", "questions": [ { "text": "Does the candidate contain exactly 12 regular pentagons and 12 regular pentagrams?", "kind": "measurement", "id": "alternating-face-test-q01" }, { "text": "Does every vertex have the cyclic configuration 5/2.5.5/2.5?", "kind": "definition", "id": "alternating-face-test-q02" } ] } ] } ] }, { "id": "incidence-and-crossings", "name": "Incidence and crossings", "description": "Preserve the mathematical connectivity through a self-intersecting realization.", "rationale": "Visible intersections can be mistaken for edges, changing the object being modelled.", "layers": [ { "id": "face-boundary-cycles", "name": "Face boundary cycles", "description": "Record pentagons and pentagrams as ordered mathematical boundaries.", "findings": [ { "id": "pentagram-traversal", "name": "Pentagram traversal", "description": "Retain the star traversal instead of substituting a convex pentagon or a subdivided outline.", "questions": [ { "text": "Does each pentagram boundary follow the {5/2} traversal through its five vertices?", "kind": "definition", "id": "pentagram-traversal-q01" }, { "text": "Are rendering subdivisions mapped back to the original pentagram face and its five edges?", "kind": "boundary", "id": "pentagram-traversal-q02" } ] } ] }, { "id": "true-adjacency", "name": "True adjacency", "description": "Separate shared edges from geometric crossings.", "findings": [ { "id": "incidence-integrity", "name": "Incidence integrity", "description": "Audit the declared connectivity independently of the displayed surface.", "questions": [ { "text": "Do the declared incidences recover 30 vertices, 60 edges, and 24 faces?", "kind": "measurement", "id": "incidence-integrity-q01" }, { "text": "Which apparent intersections are absent from the mathematical incidence structure?", "kind": "boundary", "id": "incidence-integrity-q02" }, { "text": "Does every mathematical edge connect its intended two faces without adding adjacency at crossings?", "kind": "definition", "id": "incidence-integrity-q03" } ] } ] } ] }, { "id": "metric-realization", "name": "Metric realization", "description": "Determine whether coordinates realize the uniform polyhedron at a declared scale.", "rationale": "Correct connectivity can still be embedded with distorted faces or broken symmetry.", "layers": [ { "id": "coordinates-and-scale", "name": "Coordinates and scale", "description": "Make coordinate provenance, normalization, and precision explicit.", "findings": [ { "id": "normalized-realization", "name": "Normalized realization", "description": "Establish reproducible coordinates and quantify geometric error.", "questions": [ { "text": "Which construction or coordinate source generated the realization, and what edge length normalizes it?", "kind": "provenance", "id": "normalized-realization-q01" }, { "text": "What are the maximum normalized edge-length and face-planarity residuals?", "kind": "measurement", "id": "normalized-realization-q02" } ] } ] }, { "id": "uniformity-validation", "name": "Uniformity validation", "description": "Check regularity and symmetry beyond equal edge lengths.", "findings": [ { "id": "regular-faces-and-vertex-orbits", "name": "Regular faces and vertex orbits", "description": "Require both regular face geometry and a symmetry action relating all vertices.", "questions": [ { "text": "Are the pentagon and pentagram faces regular under their respective boundary traversals?", "kind": "measurement", "id": "regular-faces-and-vertex-orbits-q01" }, { "text": "Do verified symmetries preserving the full face incidence act transitively on all 30 vertices?", "kind": "definition", "id": "regular-faces-and-vertex-orbits-q02" }, { "text": "What numerical tolerance permits accepting this approximation for the intended operation?", "kind": "action", "id": "regular-faces-and-vertex-orbits-q03" } ] } ] } ] }, { "id": "surface-interpretation", "name": "Surface interpretation", "description": "Specify what filled faces, surface measurements, and displayed fragments mean.", "rationale": "Self-intersecting faces require explicit conventions before appearance or measurements can be compared.", "layers": [ { "id": "star-face-interiors", "name": "Star-face interiors", "description": "Distinguish a pentagram boundary from a chosen filling of its plane.", "findings": [ { "id": "fill-and-orientation", "name": "Fill and orientation", "description": "Declare how the central region and overlapping regions of star faces are treated.", "questions": [ { "text": "Which fill rule determines whether the central pentagonal region of each pentagram is included?", "kind": "definition", "id": "fill-and-orientation-q01" }, { "text": "How are face orientations recorded for winding-sensitive calculations?", "kind": "measurement", "id": "fill-and-orientation-q02" } ] } ] }, { "id": "measurement-and-display", "name": "Measurement and display", "description": "Keep mathematical quantities separate from visible fragments and mesh output.", "findings": [ { "id": "interpretable-output", "name": "Interpretable output", "description": "Attach the interpretation needed to reproduce rendered or computed results.", "questions": [ { "text": "Does a reported area measure filled face regions, count overlaps with multiplicity, or measure the visible exterior?", "kind": "measurement", "id": "interpretable-output-q01" }, { "text": "What interior or winding convention defines any reported volume?", "kind": "definition", "id": "interpretable-output-q02" }, { "text": "Can an export preserve the mapping from triangulated fragments to all 24 mathematical faces?", "kind": "action", "id": "interpretable-output-q03" } ] } ] } ] }, { "id": "constructions-and-neighbours", "name": "Constructions and neighbours", "description": "Track derivations and transformations without confusing related polyhedra with this entry.", "rationale": "Construction history helps recognition, but a transformation can produce a distinct mathematical thing.", "layers": [ { "id": "construction-witness", "name": "Construction witness", "description": "Use a reproducible construction as evidence for the resulting incidence and geometry.", "findings": [ { "id": "rectification-witness", "name": "Rectification witness", "description": "Investigate the halfway truncation construction relating the great dodecahedron and small stellated dodecahedron. [Robert Webb's construction account](https://software3d.com/Dodecadodeca.php)", "questions": [ { "text": "Which starting polyhedron and truncation parameter reproduce the required alternating faces?", "kind": "provenance", "id": "rectification-witness-q01" }, { "text": "Does the constructed output pass the incidence and uniformity tests independently of its construction label?", "kind": "measurement", "id": "rectification-witness-q02" } ] } ] }, { "id": "identity-changing-operations", "name": "Identity-changing operations", "description": "Record the target and assumptions of operations that replace the original face structure.", "findings": [ { "id": "dual-and-derived-targets", "name": "Dual and derived targets", "description": "Treat the medial rhombic triacontahedron as a related dual, with a separate identity. [Robert Webb's dual identification](https://software3d.com/Dodecadodeca.php)", "questions": [ { "text": "Which duality convention and normalization are used to construct the medial rhombic triacontahedron?", "kind": "action", "id": "dual-and-derived-targets-q01" }, { "text": "After truncation, faceting, or mesh repair, does the result still satisfy this entry's defining incidence?", "kind": "boundary", "id": "dual-and-derived-targets-q02" }, { "text": "Which neighbouring registry entry should own a result that fails those identity tests?", "kind": "action", "id": "dual-and-derived-targets-q03" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-confidence-notes", "name": "Check these first", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "This description is recalled knowledge, not source-checked research.", "Face and edge counts follow the conventional treatment of star polyhedra, in which incidental geometric crossings are not additional vertices." ], "questions": [ { "id": "evidence-confidence-notes-q01", "text": "Which of these check these first hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-identifiers", "name": "Identifiers and schemes", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "scheme": "Uniform polyhedron catalogue", "value_or_pattern": "U36", "note": "Catalogue designation for the dodecadodecahedron." }, { "scheme": "Vertex configuration", "value_or_pattern": "5.5/2.5.5/2", "note": "Two pentagons and two pentagrams alternate around each vertex; 5/2 denotes a regular pentagram." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "An example in the classification and study of uniform star polyhedra.", "Physical and computer-generated models for teaching polyhedral symmetry and self-intersection." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "quantity": "Vertices", "typical_range": "30", "unit": "vertices" }, { "quantity": "Edges", "typical_range": "60", "unit": "edges" }, { "quantity": "Faces", "typical_range": "24: 12 pentagons and 12 pentagrams", "unit": "faces" }, { "quantity": "Faces incident at each vertex", "typical_range": "4", "unit": "faces" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ "Counting incidental intersections of faces or edges as additional vertices gives incorrect combinatorial counts.", "Treating the visible fragments of intersecting faces as separate faces obscures the defining pentagonal and pentagrammic faces." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Recalled without web access and unsourced; every item is a lead to verify.", "evidence": [ { "name": "Regular dodecahedron", "difference": "The regular dodecahedron is convex, with 12 pentagonal faces and three faces at each vertex; the dodecadodecahedron has 24 faces of two types and four at each vertex." }, { "name": "Great dodecahedron", "difference": "The great dodecahedron has 12 pentagonal faces and no pentagrammic faces; the dodecadodecahedron has 12 of each." }, { "name": "Small stellated dodecahedron", "difference": "The small stellated dodecahedron has 12 pentagrammic faces, with five meeting at each vertex; the dodecadodecahedron alternates pentagrams and pentagons, with four faces at each vertex." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of dodecadodecahedron this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Which exact coordinate construction should be the canonical validation reference, and what approximation tolerances suit different uses?", "How should catalogue identifiers be reconciled when an implementation's numbering differs from a published enumeration?", "Which face-filling and volume conventions should Vercy require for comparable measurements of this self-intersecting polyhedron?", "Which topological invariants should be recorded for the abstract incidence surface, and how should they be distinguished from invariants of a subdivided spatial image?", "Does the existing world-model catalogue already cover this concept, requiring this registry entry to link to that publication?" ], "statistics": { "bundles": 6, "layers": 11, "findings": 16, "questions": 30 } }