{ "model": { "rank": 6026, "code": "thing-q188745", "model_id": "vr.tr.platonic-solid", "name": "Platonic solid", "purpose": "Let an agent explain the Platonic solids and their properties, relay the proof that there are five and their symmetries from mathematical sources, describe their occurrence in nature and culture, and distinguish Platonic solids from Archimedean solids, Kepler-Poinsot polyhedra and other regular polytopes.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q188745/", "tier": 2, "score": 63, "payload": { "layer": "wikidata", "aliases": [ "regular icosahedron", "regular dodecahedron", "regular octahedron" ], "aliasCount": 3, "merged": 3, "knownIn": 63, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q188745", "url": "https://www.wikidata.org/wiki/Q188745", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T06:52:40Z", "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": 3, "engine": "claude" }, "metaModel": { "id": "THING-Q188745", "registryId": "vr.tr.platonic-solid", "name": "Platonic solid", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q188745/", "model": { "registry_id": "vr.tr.platonic-solid", "name": "Platonic solid", "purpose": "Let an agent explain the Platonic solids and their properties, relay the proof that there are five and their symmetries from mathematical sources, describe their occurrence in nature and culture, and distinguish Platonic solids from Archimedean solids, Kepler-Poinsot polyhedra and other regular polytopes.", "definition": "A convex polyhedron whose faces are congruent regular polygons meeting the same number at every vertex, of which exactly five exist, the tetrahedron with four triangles, the cube with six squares, the octahedron with eight triangles, the dodecahedron with twelve pentagons and the icosahedron with twenty triangles, known since antiquity, associated by Plato with the classical elements, proved to be the only five by Euclid, and important in geometry, crystallography, chemistry and design.", "what_it_is_for": "Not applicable; mathematical objects.", "affordances": [ "explain the five solids", "relay proofs and symmetries", "describe occurrence", "distinguish related polyhedra" ], "distinguishing_features": [ "Congruent regular faces", "Identical vertices", "Exactly five", "High symmetry" ], "appearance": "Five symmetric solids with identical regular faces.", "visual_identification": [ "Convex regular polyhedra", "Tetrahedron, cube, octahedron, dodecahedron, icosahedron", "Archimedean solids mix face types; Kepler-Poinsot polyhedra are non-convex; higher polytopes live in more dimensions" ], "physical_properties": [ { "quantity": "count", "typical_range": "5", "unit": "solids", "note": "" }, { "quantity": "Euler characteristic", "typical_range": "2", "unit": "value", "note": "V minus E plus F" }, { "quantity": "icosahedron faces", "typical_range": "20", "unit": "count", "note": "" }, { "quantity": "dodecahedron faces", "typical_range": "12", "unit": "count", "note": "" } ], "families_and_kinds": [ "regular tetrahedron", "cube or regular hexahedron", "regular octahedron", "regular dodecahedron", "regular icosahedron", "dual pairs and their symmetry groups" ], "related_models": [ { "relation": "is a kind of", "target": "regular polyhedron", "why": "in registry terms" }, { "relation": "is a kind of", "target": "convex polyhedron", "why": "in registry terms" }, { "relation": "is a kind of", "target": "regular convex polytope", "why": "in registry terms" }, { "relation": "is contrasted with", "target": "Archimedean solid", "why": "with mixed faces" } ], "identifiers": [], "standards_and_regulation": [ "No regulation; mathematical conventions" ], "failure_modes_and_hazards": [ "Confusing Platonic with Archimedean solids", "Mystical claims presented as science", "Mislabelling duals" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What Platonic solids are.", "rationale": "Science.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is a Platonic solid, and how does it differ from Archimedean, Kepler-Poinsot and higher-dimensional regular polytopes?", "kind": "definition" }, { "text": "Is the question about the five solids in general, one solid or a related polyhedron?", "kind": "boundary" } ] } ] }, { "id": "five", "name": "Five", "description": "The five solids.", "findings": [ { "id": "five-finding", "name": "Five", "description": "Five.", "questions": [ { "text": "What are the tetrahedron, cube, octahedron, dodecahedron and icosahedron, and what are their faces, vertices and edges?", "kind": "definition" }, { "text": "Which entry fits the specific solid?", "kind": "action" } ] } ] } ] }, { "id": "mathematics", "name": "Mathematics", "description": "Mathematics.", "rationale": "Science.", "layers": [ { "id": "proof", "name": "Proof", "description": "Why only five.", "findings": [ { "id": "proof-finding", "name": "Proof", "description": "Proof.", "questions": [ { "text": "How do Euclid s argument and Euler s formula show that only five Platonic solids exist?", "kind": "provenance" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "symmetry", "name": "Symmetry", "description": "Symmetry and duality.", "findings": [ { "id": "symmetry-finding", "name": "Symmetry", "description": "Symmetry.", "questions": [ { "text": "What are the symmetry groups and dual pairs of the Platonic solids?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] } ] }, { "id": "nature", "name": "Nature", "description": "Occurrence.", "rationale": "Application.", "layers": [ { "id": "science", "name": "Science", "description": "Science.", "findings": [ { "id": "science-finding", "name": "Science", "description": "Science.", "questions": [ { "text": "Where do Platonic solids appear in crystals, viruses, molecules and dice?", "kind": "provenance" }, { "text": "Which entry fits icosahedral virus?", "kind": "action" } ] } ] }, { "id": "design", "name": "Design", "description": "Design and games.", "findings": [ { "id": "design-finding", "name": "Design", "description": "Design.", "questions": [ { "text": "How are Platonic solids used in design, architecture and role-playing dice?", "kind": "provenance" }, { "text": "Which entry fits polyhedral dice?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and culture.", "rationale": "Context.", "layers": [ { "id": "history", "name": "History", "description": "History.", "findings": [ { "id": "history-finding", "name": "History", "description": "History.", "questions": [ { "text": "How did Plato, Euclid and Kepler treat the solids, and what did Kepler s model of the solar system claim?", "kind": "provenance" }, { "text": "Which entry fits Timaeus?", "kind": "action" } ] } ] }, { "id": "culture", "name": "Culture", "description": "Culture.", "findings": [ { "id": "culture-finding", "name": "Culture", "description": "Culture.", "questions": [ { "text": "How do Platonic solids appear in art and in esoteric claims, with the latter attributed and not endorsed?", "kind": "provenance" }, { "text": "Is the presentation evidence-based?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should each solid be a separate entry?", "How should mathematical sources be linked?", "The registry entry has merged aliases naming three of the five solids; should they be split off?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a Platonic solid, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain the Platonic solids and their properties, relay the proof that there are five and their symmetries from mathematical sources, describe their occurrence in nature and culture, and distinguish Platonic solids from Archimedean solids, Kepler-Poinsot polyhedra and other regular polytopes.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: regular icosahedron, regular dodecahedron, regular octahedron.", "3 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 63 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a Platonic solid, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "regular icosahedron", "regular dodecahedron", "regular octahedron" ] } ], "standing": "Described in 63 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 3 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one Platonic solid from another, and a Platonic solid from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a Platonic solid sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a Platonic solid from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a Platonic solid passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a Platonic solid between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a Platonic solid, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a Platonic solid is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What Platonic solid is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of Platonic solid are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is Platonic solid operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of Platonic solid and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of Platonic solid?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as Platonic solid?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a Platonic solid came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a Platonic solid and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a Platonic solid is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a Platonic solid, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a Platonic solid, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a Platonic solid is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }