{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.johnson-solid","code":"thing-q1059659","url":"https://ver.cy/models/thing/q1059659/","name":"Johnson solid","alternateNames":["elongated pentagonal pyramid","biaugmented triangular prism","augmented hexagonal prism","gyroelongated pentagonal pyramid","augmented dodecahedron","gyroelongated square bipyramid","elongated triangular pyramid","parabiaugmented hexagonal prism","metabiaugmented hexagonal prism","augmented tridiminished icosahedron","augmented pentagonal prism","square cupola"],"kind":"thing","status":"published","version":"0.2.0-wave.3","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"One of 92 strictly convex polyhedra with regular polygon faces that are not uniform, that is neither Platonic, Archimedean, prisms nor antiprisms, enumerated by Norman Johnson in 1966 and proved complete by Victor Zalgaller in 1969, including pyramids, cupolae, rotundae and their elongated, gyroelongated, augmented and diminished forms such as the elongated pentagonal pyramid, the augmented dodecahedron and the gyroelongated square bipyramid; Johnson solids are numbered J1 to J92.","purpose":"Let an agent define Johnson solids, explain the classification and naming scheme, identify specific solids by number and construction, and distinguish them from uniform polyhedra and near-misses.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Regular faces","Strict convexity","Non-uniform vertices","Systematic naming"],"structure":{"bundles":[{"id":"define","name":"Define","description":"Definition.","layers":[{"id":"definition","name":"Definition","description":"Definition.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What is a Johnson solid, and what conditions define the class?","kind":"definition"},{"text":"Is the solid a Johnson solid, a uniform polyhedron or a near-miss?","kind":"boundary"}]}]},{"id":"naming","name":"Naming","description":"Naming scheme.","findings":[{"id":"naming-finding","name":"Naming","description":"Naming.","questions":[{"text":"How does the naming scheme with elongated, gyroelongated, augmented and diminished work?","kind":"definition"},{"text":"Which entry fits the specific solid?","kind":"action"}]}]}]},{"id":"explore","name":"Explore","description":"The 92 solids.","layers":[{"id":"families","name":"Families","description":"Families.","findings":[{"id":"families-finding","name":"Families","description":"Families.","questions":[{"text":"What families make up the 92 solids, and how are they constructed?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"properties","name":"Properties","description":"Properties.","findings":[{"id":"properties-finding","name":"Properties","description":"Properties.","questions":[{"text":"What are the vertex, edge, face counts, symmetries and volumes of specific solids?","kind":"measurement"},{"text":"Which entry fits polyhedron geometry?","kind":"action"}]}]}]},{"id":"context","name":"Context","description":"History and proof.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Johnson enumerate the solids, and how did Zalgaller prove completeness?","kind":"provenance"},{"text":"Which sources are cited?","kind":"provenance"}]}]},{"id":"related","name":"Related","description":"Related classes.","findings":[{"id":"related-finding","name":"Related","description":"Related.","questions":[{"text":"What are near-miss Johnson solids and higher-dimensional analogues?","kind":"provenance"},{"text":"Which entry fits near-miss Johnson solid?","kind":"action"}]}]}]},{"id":"use","name":"Use","description":"Models and applications.","layers":[{"id":"models","name":"Models","description":"Making models.","findings":[{"id":"models-finding","name":"Models","description":"Models.","questions":[{"text":"How are Johnson solids modelled physically and in software?","kind":"provenance"},{"text":"Which entry fits polyhedron model?","kind":"action"}]}]},{"id":"applications","name":"Applications","description":"Applications.","findings":[{"id":"applications-finding","name":"Applications","description":"Applications.","questions":[{"text":"Where do Johnson solids appear in chemistry, architecture and design?","kind":"provenance"},{"text":"Which entry fits the specific application?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Enumerate, construct and verify the Johnson solids and their properties.","Generate nets and coordinates for teaching or modelling."],"mustNot":["Count a Platonic, Archimedean, prism or antiprism among them.","Claim a new solid in the family or a different total than the proven enumeration.","Publish geometric data without checking that faces are regular and the solid is convex.","Present a generated model as verified without a check."],"requiresHuman":["Using a generated solid as the basis of a physical structure or product."]},"ethics":{"considerations":["A mathematical enumeration is settled, and misstating it misleads learners.","Credit for the enumeration belongs to the mathematicians who proved it."],"affectedParties":["Students and teachers","Modellers and designers"]},"owners":{"steward":"Nobody: mathematical objects held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3753221","type":"parent","note":"registry parent class"},{"target":"convex polyhedron","type":"related","note":"in registry terms"},{"target":"Archimedean solid","type":"related","note":"which is uniform"},{"target":"Norman Johnson","type":"related","note":"in 1966"},{"target":"regular polygon","type":"related","note":"faces"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.johnson-solid","Wikidata: Q1059659 (https://www.wikidata.org/wiki/Q1059659)","Johnson number: J1 to J92"]},"properties":{"applicability":"not-applicable","items":["count: 92 solids","face types: 6 regular polygons - triangle, square, pentagon, hexagon, octagon, decagon"]},"recognition":{"applicability":"optional","items":["Convex, regular-faced, non-uniform polyhedra","92 solids from J1 to J92","Platonic and Archimedean solids, prisms and antiprisms are uniform and excluded","Convex solids with faces that are regular triangles, squares, pentagons, hexagons, octagons or decagons."]},"capabilities":{"applicability":"required","items":["define and classify","explain naming and construction","identify specific solids","distinguish from uniform polyhedra"]},"hazards":{"applicability":"required","items":["Confusing with near-miss Johnson solids","Naming confusion","Counting errors"]},"interfaces":{"applicability":"required","items":["No regulation; mathematical conventions"]},"context":{"applicability":"required","items":["Not applicable; a class of geometric solids.","pyramids, cupolae and rotundae","elongated and gyroelongated forms","bipyramids and bicupolae","augmented, diminished and gyrate forms of Archimedean solids","irregular members such as the snub disphenoid and bilunabirotunda"]}},"sources":[{"title":"Wikidata item Q1059659: Johnson solid","url":"https://www.wikidata.org/wiki/Q1059659","note":"identity and sense of the item"},{"title":"Wikipedia: Johnson solid","url":"https://en.wikipedia.org/wiki/Johnson_solid","note":"general description of the item"}],"openQuestions":["Should each solid be a separate entry?","How should reference tables be linked?","The registry entry has merged aliases naming specific solids; should they be split off?"],"resources":{"spec":"/models/things/publications/thing-q1059659/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q1059659/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-13T00:25:56Z","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 2026-10-06T19:51:53+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}}