{ "model": { "rank": 7481, "code": "thing-q188884", "model_id": "vr.tr.octahedron", "name": "octahedron", "purpose": "Let an agent explain octahedra and their kinds, relay properties and formulas from geometric references, describe occurrences in crystals, chemistry and games, and distinguish the regular octahedron from other eight-faced solids.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q188884/", "tier": 2, "score": 55, "payload": { "layer": "wikidata", "aliases": [ "stellated octahedron", "tetragonal trapezohedron", "elongated tetragonal disphenoid", "truncated triangular trapezohedron", "augmented triangular prism", "elongated octahedron", "triangular antiprism", "quadrilateral bipyramid", "gyrobifastigium", "tridiminished icosahedron", "Bricard octahedron", "elongated gyrobifastigium", "triangular cupola", "triangular bifrustum", "truncated tetrahedron" ], "aliasCount": 15, "merged": 15, "knownIn": 55, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": "vr.tr.octahedron", "source": { "dataset": "wikidata", "item": "Q188884", "url": "https://www.wikidata.org/wiki/Q188884", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-13T02:58:53Z", "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-Q188884", "registryId": "vr.tr.octahedron", "name": "octahedron", "version": "0.2.0-wave.3", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q188884/", "model": { "registry_id": "vr.tr.octahedron", "name": "octahedron", "purpose": "Let an agent explain octahedra and their kinds, relay properties and formulas from geometric references, describe occurrences in crystals, chemistry and games, and distinguish the regular octahedron from other eight-faced solids.", "definition": "A polyhedron with eight faces, most commonly the regular octahedron with eight equilateral triangular faces, six vertices and twelve edges, one of the five Platonic solids and the dual of the cube, but also including irregular octahedra such as the hexagonal prism, the tetragonal trapezohedron, the elongated tetragonal disphenoid, the truncated triangular trapezohedron, the augmented triangular prism and the elongated octahedron, and compounds such as the stellated octahedron; octahedra appear in crystals, molecular geometry and dice.", "what_it_is_for": "Not applicable; a geometric solid.", "affordances": [ "explain the solid and kinds", "relay properties and formulas", "describe occurrences", "distinguish regular from irregular" ], "distinguishing_features": [ "Eight faces", "Platonic regular form", "Cube duality", "Many irregular forms" ], "appearance": "Two square pyramids joined at their bases, in the regular case.", "visual_identification": [ "Eight-faced polyhedron", "Regular octahedron, trapezohedra, disphenoids, prisms, stellated octahedron", "The cube is its dual; the hexahedron has six faces; the octagon is a plane figure" ], "physical_properties": [ { "quantity": "regular octahedron faces", "typical_range": "8", "unit": "count", "note": "equilateral triangles" }, { "quantity": "vertices and edges", "typical_range": "6 and 12", "unit": "count", "note": "" }, { "quantity": "volume with edge a", "typical_range": "(sqrt 2 / 3) a^3", "unit": "formula", "note": "" }, { "quantity": "topologically distinct octahedra", "typical_range": "257", "unit": "count", "note": "convex" } ], "families_and_kinds": [ "regular octahedron", "hexagonal prism", "tetragonal trapezohedron", "elongated tetragonal disphenoid and elongated octahedron", "truncated triangular trapezohedron", "augmented triangular prism", "stellated octahedron as a compound", "octahedra in crystallography and coordination chemistry" ], "related_models": [ { "relation": "is a kind of", "target": "polyhedron", "why": "in registry terms" }, { "relation": "is a kind of", "target": "octatope", "why": "in registry terms" }, { "relation": "is the dual of", "target": "cube", "why": "in the regular case" }, { "relation": "is one of the", "target": "Platonic solid", "why": "set" } ], "identifiers": [], "standards_and_regulation": [ "No regulation; standard geometric definitions" ], "failure_modes_and_hazards": [ "Assuming all octahedra are regular", "Confusing octahedron with octagon", "Miscounting faces of compounds" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "understand", "name": "Understand", "description": "What an octahedron is.", "rationale": "Mathematics.", "layers": [ { "id": "definition", "name": "Definition", "description": "Definition.", "findings": [ { "id": "definition-finding", "name": "Definition", "description": "Definition.", "questions": [ { "text": "What is an octahedron, and what makes the regular octahedron a Platonic solid?", "kind": "definition" }, { "text": "Is the question about the regular octahedron, an irregular octahedron or an octagon?", "kind": "boundary" } ] } ] }, { "id": "kinds", "name": "Kinds", "description": "Kinds.", "findings": [ { "id": "kinds-finding", "name": "Kinds", "description": "Kinds.", "questions": [ { "text": "What other octahedra exist, such as trapezohedra, disphenoids, augmented prisms and the stellated octahedron?", "kind": "definition" }, { "text": "Which entry fits the specific solid?", "kind": "action" } ] } ] } ] }, { "id": "properties", "name": "Properties", "description": "Properties.", "rationale": "Mathematics.", "layers": [ { "id": "formulas", "name": "Formulas", "description": "Formulas.", "findings": [ { "id": "formulas-finding", "name": "Formulas", "description": "Formulas.", "questions": [ { "text": "What are the volume, surface area, angles and symmetry of the regular octahedron?", "kind": "measurement" }, { "text": "Which references are standard?", "kind": "provenance" } ] } ] }, { "id": "duality", "name": "Duality", "description": "Duality and relations.", "findings": [ { "id": "duality-finding", "name": "Duality", "description": "Duality.", "questions": [ { "text": "How does the octahedron relate to the cube, tetrahedron and other polyhedra?", "kind": "provenance" }, { "text": "Which entry fits dual polyhedron?", "kind": "action" } ] } ] } ] }, { "id": "occur", "name": "Occur", "description": "Occurrences.", "rationale": "Science.", "layers": [ { "id": "nature", "name": "Nature", "description": "Crystals and molecules.", "findings": [ { "id": "nature-finding", "name": "Nature", "description": "Nature.", "questions": [ { "text": "Where do octahedra occur in crystals such as diamond and fluorite and in molecular geometry?", "kind": "provenance" }, { "text": "Which sources are cited?", "kind": "provenance" } ] } ] }, { "id": "objects", "name": "Objects", "description": "Dice and design.", "findings": [ { "id": "objects-finding", "name": "Objects", "description": "Objects.", "questions": [ { "text": "How are octahedra used as eight-sided dice and in design and architecture?", "kind": "provenance" }, { "text": "Which entry fits polyhedral dice?", "kind": "action" } ] } ] } ] }, { "id": "context", "name": "Context", "description": "History and teaching.", "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 octahedron?", "kind": "provenance" }, { "text": "Which entry fits the history of geometry?", "kind": "action" } ] } ] }, { "id": "teaching", "name": "Teaching", "description": "Teaching.", "findings": [ { "id": "teaching-finding", "name": "Teaching", "description": "Teaching.", "questions": [ { "text": "How are octahedra built and taught with nets and models?", "kind": "provenance" }, { "text": "Which entry fits mathematics education?", "kind": "action" } ] } ] } ] } ] }, "openQuestions": [ "Should regular octahedron and stellated octahedron be separate entries?", "How should geometric references be linked?", "The registry entry has merged aliases naming distinct 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 octahedron, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain octahedra and their kinds, relay properties and formulas from geometric references, describe occurrences in crystals, chemistry and games, and distinguish the regular octahedron from other eight-faced solids.", "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: stellated octahedron, tetragonal trapezohedron, elongated tetragonal disphenoid, truncated triangular trapezohedron, augmented triangular prism, elongated octahedron, triangular antiprism, quadrilateral bipyramid, gyrobifastigium, tridiminished icosahedron, Bricard octahedron, elongated gyrobifastigium.", "15 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 55 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 octahedron, 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": [ "stellated octahedron", "tetragonal trapezohedron", "elongated tetragonal disphenoid", "truncated triangular trapezohedron", "augmented triangular prism", "elongated octahedron", "triangular antiprism", "quadrilateral bipyramid", "gyrobifastigium", "tridiminished icosahedron", "Bricard octahedron", "elongated gyrobifastigium" ] } ], "standing": "Described in 55 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 15 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 octahedron from another, and a octahedron 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 octahedron, 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 octahedron, 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 octahedron 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 octahedron, 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 octahedron, 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 octahedron 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 octahedron 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 octahedron, 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 octahedron, 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 octahedron 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 octahedron from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a octahedron, 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 octahedron, 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 octahedron 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 octahedron 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 octahedron between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a octahedron, 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 octahedron, 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 octahedron 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 octahedron, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a octahedron 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 octahedron, 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 octahedron, 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 octahedron 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 octahedron 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 octahedron 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 octahedron 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 octahedron 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 octahedron?", "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 octahedron?", "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 octahedron 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 octahedron and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a octahedron, 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 octahedron, 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 octahedron 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 octahedron is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a octahedron, 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 octahedron, 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 octahedron 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 } } } }