{ "model": { "rank": 10383, "code": "thing-q214856", "model_id": "vr.tr.tessellation", "name": "tessellation", "purpose": "Let an agent explain tessellations and their classification, identify or construct tilings, describe their appearance in art and nature, and support learning and computational use.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q214856/", "tier": 2, "score": 45, "payload": { "layer": "wikidata", "aliases": [ "ditrigonary trigonal hemiapeirogonal tesselation", "trigonal hemiapeirogonal tesselation", "petrial triangular tiling", "hexagonal hemiapeirogonal tesselation", "square hemiapeirogonal tesselation", "uniform honeycomb dual", "monohedral tiling", "polyhedral tiling", "snub hexagonal tiling", "snub square tiling", "demiregular tiling", "Augmented truncated hexagonal tiling", "domino tiling", "uniform tessellation", "tiling by regular polygons", "Elongated triangular tiling", "trihexagonal tiling", "pentagon tiling", "Wang tile", "apeirogonal antiprism", "Gilbert tessellation", "pinwheel tiling", "Order 3-7 kisrhombille", "Pythagorean tiling", "quasiperiodic tiling", "rhombille tiling", "aperiodic tiling", "Snub trioctagonal tiling", "sphinx tiling", "substitution tiling", "tiling with rectangles", "Truncated triheptagonal tiling", "Socolar tiling", "Ammann–Beenker tiling", "quaquaversal tiling" ], "aliasCount": 35, "merged": 35, "knownIn": 45, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q214856", "url": "https://www.wikidata.org/wiki/Q214856", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T21:59:31Z", "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": 2, "engine": "claude" }, "metaModel": { "id": "THING-Q214856", "registryId": "vr.tr.tessellation", "name": "tessellation", "version": "0.2.0-wave.2", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q214856/", "model": { "registry_id": "vr.tr.tessellation", "name": "tessellation", "purpose": "Let an agent explain tessellations and their classification, identify or construct tilings, describe their appearance in art and nature, and support learning and computational use.", "definition": "A covering of a plane or other space by shapes called tiles with no gaps or overlaps, including regular and semiregular tilings by polygons, periodic and aperiodic tilings such as Penrose tilings, tilings of the sphere and hyperbolic plane, and higher-dimensional honeycombs; tessellations are studied in geometry, appear in art, architecture and nature, and are used in computing and manufacturing.", "what_it_is_for": "Covering space with tiles.", "affordances": [ "explain tessellation types and classification", "identify or construct a tiling", "describe tessellations in art and nature", "support computational use" ], "distinguishing_features": [ "Gapless covering", "Classified by symmetry", "Periodic or aperiodic", "Generalises to other spaces" ], "appearance": "Repeating or patterned shapes covering a surface without gaps.", "visual_identification": [ "No gaps or overlaps", "Regular, semiregular or irregular", "A pattern with gaps is not a tessellation" ], "physical_properties": [], "families_and_kinds": [ "regular and semiregular tilings", "periodic tilings and wallpaper groups", "aperiodic tilings", "spherical and hyperbolic tilings", "honeycombs in higher dimensions" ], "related_models": [ { "relation": "is a kind of", "target": "polytope", "why": "category" }, { "relation": "is a kind of", "target": "cover", "why": "category" }, { "relation": "is related to", "target": "dimension", "why": "tilings by dimension" }, { "relation": "is related to", "target": "applied arts", "why": "decorative tilings" } ], "identifiers": [], "standards_and_regulation": [ "Mathematical naming conventions such as vertex configurations", "No regulation" ], "failure_modes_and_hazards": [ "Confusing tilings with patterns that have gaps", "Misnaming uniform tilings", "Overlooking aperiodic cases" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "classify", "name": "Classify", "description": "Kinds of tessellation.", "rationale": "Geometry.", "layers": [ { "id": "types", "name": "Types", "description": "Classification.", "findings": [ { "id": "types-finding", "name": "Types", "description": "Classification.", "questions": [ { "text": "What kind of tessellation is this, and how is it named by vertex configuration or symmetry group?", "kind": "definition" }, { "text": "Which regular and semiregular tilings exist?", "kind": "definition" } ] } ] }, { "id": "aperiodic", "name": "Aperiodic", "description": "Aperiodic tilings.", "findings": [ { "id": "aperiodic-finding", "name": "Aperiodic", "description": "Aperiodic.", "questions": [ { "text": "What are aperiodic tilings such as Penrose tilings and the recently found aperiodic monotile?", "kind": "provenance" }, { "text": "Why do they matter?", "kind": "provenance" } ] } ] } ] }, { "id": "construct", "name": "Construct", "description": "Making tilings.", "rationale": "Practice.", "layers": [ { "id": "build", "name": "Build", "description": "Constructing a tiling.", "findings": [ { "id": "build-finding", "name": "Build", "description": "Construction.", "questions": [ { "text": "How can a tessellation be constructed from a given shape or symmetry?", "kind": "action" }, { "text": "Which shapes tile the plane?", "kind": "definition" } ] } ] }, { "id": "compute", "name": "Compute", "description": "Computational tilings.", "findings": [ { "id": "compute-finding", "name": "Compute", "description": "Computation.", "questions": [ { "text": "How are tessellations used in computer graphics, meshing and manufacturing?", "kind": "provenance" }, { "text": "Which algorithms generate them?", "kind": "provenance" } ] } ] } ] }, { "id": "beyond", "name": "Beyond", "description": "Other spaces.", "rationale": "Generalisation.", "layers": [ { "id": "spherical", "name": "Spherical", "description": "Sphere and hyperbolic plane.", "findings": [ { "id": "spherical-finding", "name": "Spherical", "description": "Other geometries.", "questions": [ { "text": "How do tilings of the sphere and hyperbolic plane differ from planar tilings, and what are hemiapeirogonal tilings?", "kind": "definition" }, { "text": "How do they relate to polyhedra?", "kind": "definition" } ] } ] }, { "id": "honeycombs", "name": "Honeycombs", "description": "Higher dimensions.", "findings": [ { "id": "honeycombs-finding", "name": "Honeycombs", "description": "Honeycombs.", "questions": [ { "text": "What are honeycombs in three and more dimensions, and how are their duals defined?", "kind": "definition" }, { "text": "Which uniform honeycombs exist?", "kind": "provenance" } ] } ] } ] }, { "id": "culture", "name": "Culture", "description": "Art, nature and teaching.", "rationale": "Context.", "layers": [ { "id": "art", "name": "Art", "description": "Tessellations in art and nature.", "findings": [ { "id": "art-finding", "name": "Art", "description": "Art and nature.", "questions": [ { "text": "How do tessellations appear in Islamic art, Escher work, architecture and nature such as honeycombs?", "kind": "provenance" }, { "text": "Which entry fits a specific work?", "kind": "action" } ] } ] }, { "id": "teach", "name": "Teach", "description": "Teaching.", "findings": [ { "id": "teach-finding", "name": "Teach", "description": "Teaching.", "questions": [ { "text": "How can tessellations be taught with hands-on activities?", "kind": "action" }, { "text": "Which misconceptions arise?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Should wallpaper groups be a separate entry?", "How should tiling catalogues be linked?", "How should art examples be linked?" ], "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 tessellation, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain tessellations and their classification, identify or construct tilings, describe their appearance in art and nature, and support learning and computational use.", "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: ditrigonary trigonal hemiapeirogonal tesselation, trigonal hemiapeirogonal tesselation, petrial triangular tiling, hexagonal hemiapeirogonal tesselation, square hemiapeirogonal tesselation, uniform honeycomb dual, monohedral tiling, polyhedral tiling, snub hexagonal tiling, snub square tiling, demiregular tiling, Augmented truncated hexagonal tiling.", "35 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 45 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 tessellation, 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": [ "ditrigonary trigonal hemiapeirogonal tesselation", "trigonal hemiapeirogonal tesselation", "petrial triangular tiling", "hexagonal hemiapeirogonal tesselation", "square hemiapeirogonal tesselation", "uniform honeycomb dual", "monohedral tiling", "polyhedral tiling", "snub hexagonal tiling", "snub square tiling", "demiregular tiling", "Augmented truncated hexagonal tiling" ] } ], "standing": "Described in 45 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 35 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 tessellation from another, and a tessellation 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 tessellation, 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 tessellation, 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 tessellation 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 tessellation, 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 tessellation, 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 tessellation 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 tessellation 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 tessellation, 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 tessellation, 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 tessellation 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 tessellation from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a tessellation, 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 tessellation, 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 tessellation 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 tessellation 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 tessellation between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a tessellation, 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 tessellation, 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 tessellation 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 tessellation, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a tessellation 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 tessellation, 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 tessellation, 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 tessellation 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 tessellation 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 tessellation 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 tessellation 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 tessellation 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 tessellation?", "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 tessellation?", "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 tessellation 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 tessellation and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a tessellation, 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 tessellation, 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 tessellation 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 tessellation is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a tessellation, 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 tessellation, 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 tessellation 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 } } } }