{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.polygon","code":"thing-q37555","url":"https://ver.cy/models/thing/q37555/","name":"polygon","alternateNames":["apeirogon","pseudogon","◊","teragon","polyomino","dodecomino","decomino","hexomino","heptomino","octomino","tromino","nonomino"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A plane figure bounded by a finite chain of straight line segments closing in a loop, such as triangles, quadrilaterals, pentagons and hexagons; extended notions include apeirogons and polyominoes built from squares.","purpose":"Let an agent handle polygons by sides, angles, regularity, convexity and area, and link extended notions appropriately.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["A polygon has straight sides forming a closed boundary.","A simple polygon with n sides has an interior angle sum of (n - 2) x 180 degrees.","Polygons can be classified by regularity and as convex or concave.","Self-intersecting forms exist."],"structure":{"bundles":[{"id":"shape","name":"Shape","description":"Which polygon.","layers":[{"id":"sides","name":"Sides","description":"Count.","findings":[{"id":"sides-finding","name":"Sides","description":"Sides.","questions":[{"text":"How many sides does it have?","kind":"measurement"},{"text":"Is it regular?","kind":"boundary"}]}]},{"id":"convexity","name":"Convexity","description":"Convex or concave.","findings":[{"id":"convexity-finding","name":"Convexity","description":"Convexity.","questions":[{"text":"Is it convex, concave or self-intersecting?","kind":"definition"},{"text":"How does that affect calculations?","kind":"boundary"}]}]}]},{"id":"measures","name":"Measures","description":"Area and angles.","layers":[{"id":"area","name":"Area","description":"Formula.","findings":[{"id":"area-finding","name":"Area","description":"Area.","questions":[{"text":"What is its area?","kind":"measurement"},{"text":"Which formula is used?","kind":"definition"}]}]},{"id":"angles","name":"Angles","description":"Interior sum.","findings":[{"id":"angles-finding","name":"Angles","description":"Angles.","questions":[{"text":"What are its interior angles?","kind":"measurement"},{"text":"What is their sum?","kind":"measurement"}]}]}]},{"id":"computing","name":"Computing","description":"Graphics and GIS.","layers":[{"id":"graphics","name":"Graphics","description":"Triangulation.","findings":[{"id":"graphics-finding","name":"Graphics","description":"Graphics.","questions":[{"text":"How is it triangulated for rendering?","kind":"action"},{"text":"Is winding order consistent?","kind":"boundary"}]}]},{"id":"gis","name":"GIS","description":"Geometries.","findings":[{"id":"gis-finding","name":"GIS","description":"GIS polygons.","questions":[{"text":"Is the polygon valid under the GIS standard?","kind":"boundary"},{"text":"In which coordinate system?","kind":"definition"}]}]}]},{"id":"tiling","name":"Tiling","description":"Patterns.","layers":[{"id":"tiles","name":"Tiles","description":"Tessellation.","findings":[{"id":"tiles-finding","name":"Tiles","description":"Tiling.","questions":[{"text":"Can this polygon tile the plane?","kind":"boundary"},{"text":"In which pattern?","kind":"definition"}]}]},{"id":"related","name":"Related shapes","description":"Polyominoes.","findings":[{"id":"related-finding","name":"Related","description":"Related shapes.","questions":[{"text":"Is a polyomino or apeirogon meant instead?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Compute areas, angles and properties of polygons.","Validate that polygons in map or design data are closed and not self-intersecting."],"mustNot":["Present an invalid polygon as valid in map or design data others rely on.","Alter property or boundary polygons without the owner's authority.","Copy textbook solutions as a student's own work in graded assessment."],"requiresHuman":["Changing boundary polygons in land or administrative records."]},"ethics":{"considerations":["Polygons in maps define land and boundaries, so errors can affect people's property."],"affectedParties":["Students","Landowners","Users of mapping data"]},"owners":{"steward":"Nobody owns it; the owner of each dataset answers for its polygons.","roles":[],"masterSystems":[]},"relations":[{"target":"Q4365210","type":"parent","note":"registry parent class"},{"target":"Q4381515","type":"parent","note":"registry parent class"},{"target":"Q7520906","type":"parent","note":"registry parent class"},{"target":"Q78262214","type":"parent","note":"registry parent class"},{"target":"plane figure","type":"related","note":"category"},{"target":"square","type":"related","note":"example"},{"target":"polyhedron","type":"related","note":"solids"},{"target":"computer graphics and GIS","type":"related","note":"applications"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.polygon","Wikidata: Q37555 (https://www.wikidata.org/wiki/Q37555)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Number of sides","Names such as hexagon","Polyominoes are shapes made of squares","Closed flat shapes with straight sides."]},"capabilities":{"applicability":"required","items":["compute area and perimeter","classify by sides and angles","triangulate for graphics","tile the plane with suitable polygons"]},"hazards":{"applicability":"required","items":["Area errors for self-intersecting polygons","Winding-order errors in GIS"]},"interfaces":{"applicability":"required","items":["OGC Simple Features for polygons in GIS"]},"context":{"applicability":"required","items":["Geometry, design, computer graphics, mapping and tiling.","triangles","quadrilaterals","regular polygons","star polygons","polyominoes (related)"]}},"sources":[{"title":"Wikidata item Q37555: polygon","url":"https://www.wikidata.org/wiki/Q37555","note":"identity and sense of the item"},{"title":"Wikipedia: Polygon","url":"https://en.wikipedia.org/wiki/Polygon","note":"general description of the item"}],"openQuestions":["Should polygon types be separate entries?","How should GIS polygons be linked?","How should polyominoes be split off?"],"resources":{"spec":"/models/things/publications/thing-q37555/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q37555/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T07:15:41Z","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":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:30+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}