{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.dodecadodecahedron","code":"thing-q3033696","url":"https://ver.cy/models/thing/q3033696/","name":"dodecadodecahedron","alternateNames":[],"kind":"thing","status":"published","version":"0.1.0-research.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"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.","purpose":"Enable an agent to recognise a dodecadodecahedron, validate its geometric representation, and choose operations that preserve or explicitly transform its identity.","scope":{"in":["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":["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"],"boundaries":[]},"distinguishingFeatures":["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."],"structure":{"bundles":[{"id":"identity-and-recognition","name":"Identity and recognition","description":"Establish whether a named or supplied object represents the registered dodecadodecahedron.","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?","id":"catalogue-identity-q01","kind":"provenance"},{"text":"Does a qualified name denote this same object or a snub, truncated, or ditrigonal neighbour?","id":"catalogue-identity-q02","kind":"boundary"}]}]},{"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?","id":"alternating-face-test-q01","kind":"measurement"},{"text":"Does every vertex have the cyclic configuration 5/2.5.5/2.5?","id":"alternating-face-test-q02","kind":"definition"}]}]}]},{"id":"incidence-and-crossings","name":"Incidence and crossings","description":"Preserve the mathematical connectivity through a self-intersecting realization.","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?","id":"pentagram-traversal-q01","kind":"definition"},{"text":"Are rendering subdivisions mapped back to the original pentagram face and its five edges?","id":"pentagram-traversal-q02","kind":"boundary"}]}]},{"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?","id":"incidence-integrity-q01","kind":"measurement"},{"text":"Which apparent intersections are absent from the mathematical incidence structure?","id":"incidence-integrity-q02","kind":"boundary"},{"text":"Does every mathematical edge connect its intended two faces without adding adjacency at crossings?","id":"incidence-integrity-q03","kind":"definition"}]}]}]},{"id":"metric-realization","name":"Metric realization","description":"Determine whether coordinates realize the uniform polyhedron at a declared scale.","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?","id":"normalized-realization-q01","kind":"provenance"},{"text":"What are the maximum normalized edge-length and face-planarity residuals?","id":"normalized-realization-q02","kind":"measurement"}]}]},{"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?","id":"regular-faces-and-vertex-orbits-q01","kind":"measurement"},{"text":"Do verified symmetries preserving the full face incidence act transitively on all 30 vertices?","id":"regular-faces-and-vertex-orbits-q02","kind":"definition"},{"text":"What numerical tolerance permits accepting this approximation for the intended operation?","id":"regular-faces-and-vertex-orbits-q03","kind":"action"}]}]}]},{"id":"surface-interpretation","name":"Surface interpretation","description":"Specify what filled faces, surface measurements, and displayed fragments mean.","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?","id":"fill-and-orientation-q01","kind":"definition"},{"text":"How are face orientations recorded for winding-sensitive calculations?","id":"fill-and-orientation-q02","kind":"measurement"}]}]},{"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?","id":"interpretable-output-q01","kind":"measurement"},{"text":"What interior or winding convention defines any reported volume?","id":"interpretable-output-q02","kind":"definition"},{"text":"Can an export preserve the mapping from triangulated fragments to all 24 mathematical faces?","id":"interpretable-output-q03","kind":"action"}]}]}]},{"id":"constructions-and-neighbours","name":"Constructions and neighbours","description":"Track derivations and transformations without confusing related polyhedra with this entry.","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?","id":"rectification-witness-q01","kind":"provenance"},{"text":"Does the constructed output pass the incidence and uniformity tests independently of its construction label?","id":"rectification-witness-q02","kind":"measurement"}]}]},{"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?","id":"dual-and-derived-targets-q01","kind":"action"},{"text":"After truncation, faceting, or mesh repair, does the result still satisfy this entry's defining incidence?","id":"dual-and-derived-targets-q02","kind":"boundary"},{"text":"Which neighbouring registry entry should own a result that fails those identity tests?","id":"dual-and-derived-targets-q03","kind":"action"}]}]}]},{"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.","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.","questions":[{"text":"Which of these check these first hold for the sense of dodecadodecahedron this model covers, and on what evidence?","id":"evidence-confidence-notes-q01","kind":"provenance"}]},{"id":"evidence-identifiers","name":"Identifiers and schemes","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these identifiers and schemes hold for the sense of dodecadodecahedron this model covers, and on what evidence?","id":"evidence-identifiers-q01","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.","questions":[{"text":"Which of these real-world use hold for the sense of dodecadodecahedron this model covers, and on what evidence?","id":"evidence-real-world-use-q01","kind":"provenance"}]},{"id":"evidence-measurements","name":"Typical measurements","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these typical measurements hold for the sense of dodecadodecahedron this model covers, and on what evidence?","id":"evidence-measurements-q01","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.","questions":[{"text":"Which of these failure modes and hazards hold for the sense of dodecadodecahedron this model covers, and on what evidence?","id":"evidence-failure-modes-and-hazards-q01","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.","questions":[{"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?","id":"evidence-neighbours-q01","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain the dodecadodecahedron's faces, vertex figure and relation to other uniform polyhedra.","Generate accurate models or images of it from verified coordinates."],"mustNot":["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."],"requiresHuman":["Publishing new claims about its properties under a person's name."]},"ethics":{"considerations":["Accuracy and credit matter in mathematical teaching and publication."],"affectedParties":["Students","Mathematicians","Model makers"]},"owners":{"steward":"Nobody owns it; it is a concept of geometry.","roles":[],"masterSystems":[]},"relations":[{"target":"Q2878957","type":"parent","note":"registry parent class"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.dodecadodecahedron","Wikidata: Q3033696 (https://www.wikidata.org/wiki/Q3033696)"]},"properties":{"applicability":"not-applicable","items":["Face inventory: 12 pentagons {5} and 12 pentagrams {5/2}","Incidence counts: 30 vertices; 60 edges; 24 faces","Cyclic vertex configuration: 5/2.5.5/2.5, up to cyclic rotation and reversal","Edge scale: Positive edge length a; dimensionless normalization or declared length unit","Regularity residual: Maximum relative edge-length deviation and face-planarity residual divided by a","Representation validity: Unverified; incidence-validated; geometry-validated; rejected","Face-interior interpretation: Boundary-only; even-odd fill; winding-based fill; explicitly specified alternative"]},"recognition":{"applicability":"optional","items":["Twelve pentagons and twelve pentagrams crossing through each other, four faces at each vertex."]},"capabilities":{"applicability":"required","items":["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"]},"hazards":{"applicability":"required","items":["Self-intersecting faces are easily mis-rendered by software."]},"interfaces":{"applicability":"not-applicable","items":[]},"context":{"applicability":"required","items":["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."]}},"sources":[{"title":"Wikidata item Q3033696: dodecadodecahedron","url":"https://www.wikidata.org/wiki/Q3033696","note":"identity and sense of the item"},{"title":"Wikipedia: Dodecadodecahedron","url":"https://en.wikipedia.org/wiki/Dodecadodecahedron","note":"general description of the item"}],"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?"],"resources":{"spec":"/models/things/publications/thing-q3033696/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q3033696/spec.json"],"providers":["Codex"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T09:17:06Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"not-applicable","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:29+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties.","interaction.interfaces":"No specific standard, law or official classification applies to this abstract polyhedron as such."},"score":1.0}}