Johnson solid
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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define Definition.
Definition
Definition.
Definition
Definition.
- What is a Johnson solid, and what conditions define the class? definition
- Is the solid a Johnson solid, a uniform polyhedron or a near-miss? boundary
Naming
Naming scheme.
Naming
Naming.
- How does the naming scheme with elongated, gyroelongated, augmented and diminished work? definition
- Which entry fits the specific solid? action
Explore The 92 solids.
Families
Families.
Families
Families.
- What families make up the 92 solids, and how are they constructed? provenance
- Which references are standard? provenance
Properties
Properties.
Properties
Properties.
- What are the vertex, edge, face counts, symmetries and volumes of specific solids? measurement
- Which entry fits polyhedron geometry? action
Context History and proof.
History
History.
History
History.
- How did Johnson enumerate the solids, and how did Zalgaller prove completeness? provenance
- Which sources are cited? provenance
Related
Related classes.
Related
Related.
- What are near-miss Johnson solids and higher-dimensional analogues? provenance
- Which entry fits near-miss Johnson solid? action
Use Models and applications.
Models
Making models.
Models
Models.
- How are Johnson solids modelled physically and in software? provenance
- Which entry fits polyhedron model? action
Applications
Applications.
Applications
Applications.
- Where do Johnson solids appear in chemistry, architecture and design? provenance
- Which entry fits the specific application? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- 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
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Regular faces
- Strict convexity
- Non-uniform vertices
- Systematic naming
What robots and AI may and may not do Filled
Must not
- 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.
Only with a human decision
- Using a generated solid as the basis of a physical structure or product.
May
- Enumerate, construct and verify the Johnson solids and their properties.
- Generate nets and coordinates for teaching or modelling.
Moral aspects Filled
- A mathematical enumeration is settled, and misstating it misleads learners.
- Credit for the enumeration belongs to the mathematicians who proved it.
Who is affected
- Students and teachers
- Modellers and designers
Owners Filled
Steward
Nobody: mathematical objects held in common.
Links to other meta-models Filled
parent
- Q3753221 - registry parent class
related
- convex polyhedron - in registry terms
- Archimedean solid - which is uniform
- Norman Johnson - in 1966
- regular polygon - faces
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.johnson-solid
- Wikidata: Q1059659 (https://www.wikidata.org/wiki/Q1059659)
- Johnson number: J1 to J92
Direct properties not applicable Not applicable
- count: 92 solids
- face types: 6 regular polygons - triangle, square, pentagon, hexagon, octagon, decagon
Plane XCT: no invented physical properties.
Recognition optional Filled
- 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 and actions required Filled
- define and classify
- explain naming and construction
- identify specific solids
- distinguish from uniform polyhedra
Hazards and failure modes required Filled
- Confusing with near-miss Johnson solids
- Naming confusion
- Counting errors
Standards and interfaces required Filled
- No regulation; mathematical conventions
Context of use required Filled
- 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 Filled
- Wikidata item Q1059659: Johnson solid - identity and sense of the item
- Wikipedia: Johnson solid - general description of the item
Open questions
- 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?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1059659/spec.json