prismatoid
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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What a prismatoid is.
Definition
Definition.
Definition
Definition.
- What is a prismatoid, and how does it differ from a prism, prismoid and general polyhedron? definition
- Is the question about the definition, volume, a specific solid or star forms? boundary
Kinds
Kinds.
Kinds
Kinds.
- What are cupolae, heptagrammic cupolae, pentagrammic cuploids and antipyramids? definition
- Which entry fits the specific solid? action
Geometry Geometry.
Volume
Volume formula.
Volume
Volume.
- How is the prismatoid formula derived and applied? provenance
- Which references are standard? provenance
Convexity
Convexity.
Convexity
Convexity.
- Which prismatoids are convex, and how do star polygon bases change this? provenance
- Which sources are cited? provenance
Applications Applications.
Engineering
Earthwork volumes.
Engineering
Engineering.
- How is the prismoidal formula used in earthwork volume estimates? provenance
- Which entry fits earthworks (engineering)? action
Models
Models.
Models
Models.
- How are star cupolae studied and visualised? provenance
- Which entry fits star polygon? action
Context History.
History
History.
History
History.
- How did the prismatoid formula develop? provenance
- Which entry fits the history of geometry? action
Related
Related solids.
Related
Related.
- How do Johnson solids relate to cupolae? provenance
- Which entry fits Johnson solid? action
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- pentagrammic cuploid, Heptagrammic cupola, cupola, {7/3} heptagram cupola, {7/5} heptagram cupola, antipyramid
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Two parallel planes
- Simple volume formula
- Many familiar solids
- Star generalisations
What robots and AI may and may not do Filled
Must not
- Assume all prismatoids are convex.
- Apply the volume formula to shapes it does not cover.
- Present exotic star forms as standard.
Only with a human decision
- Relying on computed volumes in engineering.
May
- Explain prismatoids and the prismatoid formula, citing geometry sources.
- Distinguish prismatoids from prismoids.
Moral aspects Filled
- Geometric errors in volume can cause material or safety errors.
- Learners need accurate definitions.
Who is affected
- Students
- Engineers
Owners Filled
Steward
Nobody owns mathematical concepts; they are held in common.
Links to other meta-models Filled
parent
- Q3753221 - registry parent class
related
- polyhedron - in geometry
- convex polyhedron - in registry terms, not true of star forms
- cupola
- antiprism
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.prismatoid
- Wikidata: Q1757451 (https://www.wikidata.org/wiki/Q1757451)
Direct properties not applicable Not applicable
- volume formula: V = h(A1 + 4M + A2)/6 note
- examples: prism, pyramid, cupola, frustum list
- star variants: non-convex note
Plane XCT: no invented physical properties.
Recognition optional Filled
- 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 and actions required Filled
- explain the definition
- relay the volume formula
- describe kinds
- distinguish related solids
Hazards and failure modes required Filled
- Assuming all prismatoids are convex
- Confusing prismatoid and prismoid
- Registry aliases naming exotic star forms
Standards and interfaces required Filled
- No regulation
Context of use required Filled
- Not applicable; a geometric solid.
- prisms and antiprisms
- pyramids and frusta
- wedges
- cupolae
- star cupolae and cuploids
- antipyramids
Sources Filled
- Wikidata item Q1757451: prismatoid - identity and sense of the item
- Wikipedia: Prismatoid - general description of the item
Open questions
- Should star cupolae be separate entries?
- How should geometry references be linked?
- The registry parent convex polyhedron excludes star variants; should it be reviewed?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q1757451/spec.json