{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.prismatoid","code":"thing-q1757451","url":"https://ver.cy/models/thing/q1757451/","name":"prismatoid","alternateNames":["pentagrammic cuploid","Heptagrammic cupola","cupola","{7/3} heptagram cupola","{7/5} heptagram cupola","antipyramid"],"kind":"thing","status":"published","version":"0.2.0-wave.4","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A polyhedron whose vertices all lie in two parallel planes, including prisms, antiprisms, pyramids, wedges, frusta and cupolae, and generalisations with star polygon bases such as heptagrammic cupolae, the {7/3} and {7/5} heptagram cupolae and pentagrammic cuploids; antipyramids are not generally prismatoids and qualify only if their vertices satisfy the two-plane condition; the prismatoid formula gives the volume from the areas of the two bases and the mid-section where its assumptions apply.","purpose":"Let an agent explain prismatoids and their kinds, relay the prismatoid volume formula and examples from geometry references, describe the star cupolae and cuploids the registry aliases name, and distinguish prismatoids from prisms, general polyhedra and prismoids, noting the convexity issue.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Two parallel planes","Simple volume formula","Many familiar solids","Star generalisations"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a prismatoid is.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a prismatoid, and how does it differ from a prism, prismoid and general polyhedron?","kind":"definition"},{"text":"Is the question about the definition, volume, a specific solid or star forms?","kind":"boundary"}]}]},{"id":"kinds","name":"Kinds","description":"Kinds.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Kinds.","questions":[{"text":"What are cupolae, heptagrammic cupolae, pentagrammic cuploids and antipyramids?","kind":"definition"},{"text":"Which entry fits the specific solid?","kind":"action"}]}]}]},{"id":"geometry","name":"Geometry","description":"Geometry.","layers":[{"id":"volume","name":"Volume","description":"Volume formula.","findings":[{"id":"volume-finding","name":"Volume","description":"Volume.","questions":[{"text":"How is the prismatoid formula derived and applied?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"convexity","name":"Convexity","description":"Convexity.","findings":[{"id":"convexity-finding","name":"Convexity","description":"Convexity.","questions":[{"text":"Which prismatoids are convex, and how do star polygon bases change this?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]}]},{"id":"applications","name":"Applications","description":"Applications.","layers":[{"id":"engineering","name":"Engineering","description":"Earthwork volumes.","findings":[{"id":"engineering-finding","name":"Engineering","description":"Engineering.","questions":[{"text":"How is the prismoidal formula used in earthwork volume estimates?","kind":"provenance"},{"text":"Which entry fits earthworks (engineering)?","kind":"action"}]}]},{"id":"models","name":"Models","description":"Models.","findings":[{"id":"models-finding","name":"Models","description":"Models.","questions":[{"text":"How are star cupolae studied and visualised?","kind":"provenance"},{"text":"Which entry fits star polygon?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"History.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the prismatoid formula develop?","kind":"provenance"},{"text":"Which entry fits the history of geometry?","kind":"action"}]}]},{"id":"related","name":"Related","description":"Related solids.","findings":[{"id":"related-finding","name":"Related","description":"Related.","questions":[{"text":"How do Johnson solids relate to cupolae?","kind":"provenance"},{"text":"Which entry fits Johnson solid?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Explain prismatoids and the prismatoid formula, citing geometry sources.","Distinguish prismatoids from prismoids."],"mustNot":["Assume all prismatoids are convex.","Apply the volume formula to shapes it does not cover.","Present exotic star forms as standard."],"requiresHuman":["Relying on computed volumes in engineering."]},"ethics":{"considerations":["Geometric errors in volume can cause material or safety errors.","Learners need accurate definitions."],"affectedParties":["Students","Engineers"]},"owners":{"steward":"Nobody owns mathematical concepts; they are held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3753221","type":"parent","note":"registry parent class"},{"target":"polyhedron","type":"related","note":"in geometry"},{"target":"convex polyhedron","type":"related","note":"in registry terms, not true of star forms"},{"target":"cupola","type":"related"},{"target":"antiprism","type":"related"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.prismatoid","Wikidata: Q1757451 (https://www.wikidata.org/wiki/Q1757451)"]},"properties":{"applicability":"not-applicable","items":["volume formula: V = h(A1 + 4M + A2)/6 note","examples: prism, pyramid, cupola, frustum list","star variants: non-convex note"]},"recognition":{"applicability":"optional","items":["A prismatoid has all its vertices in two parallel planes.","Examples include prisms, antiprisms, pyramids, cupolae and star forms that satisfy the two-plane condition.","Antipyramids are not generally prismatoids and must be assessed against the two-plane condition.","Prisms have congruent bases, general polyhedra need not satisfy the two-plane condition, and prismoids are a narrower class.","A solid with two parallel faces joined by triangles, quadrilaterals or other polygons."]},"capabilities":{"applicability":"required","items":["explain the definition","relay the volume formula","describe kinds","distinguish related solids"]},"hazards":{"applicability":"required","items":["Assuming all prismatoids are convex","Confusing prismatoid and prismoid","Registry aliases naming exotic star forms"]},"interfaces":{"applicability":"required","items":["No regulation"]},"context":{"applicability":"required","items":["Not applicable; a geometric solid.","prisms and antiprisms","pyramids and frusta","wedges","cupolae","star cupolae and cuploids","antipyramids"]}},"sources":[{"title":"Wikidata item Q1757451: prismatoid","url":"https://www.wikidata.org/wiki/Q1757451","note":"identity and sense of the item"},{"title":"Wikipedia: Prismatoid","url":"https://en.wikipedia.org/wiki/Prismatoid","note":"general description of the item"}],"openQuestions":["Should star cupolae be separate entries?","How should geometry references be linked?","The registry parent convex polyhedron excludes star variants; should it be reviewed?"],"resources":{"spec":"/models/things/publications/thing-q1757451/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1757451/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T18:31:19Z","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 2026-10-07T10:10:26+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}}