Archimedean solid
Let an agent explain Archimedean solids, relay their definition, the thirteen solids, symmetry and duals from geometry sources, describe the named examples, and distinguish Archimedean solids from Platonic solids, Johnson solids, Catalan solids and prisms and antiprisms.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain Archimedean solids, relay their definition, the thirteen solids, symmetry and duals from geometry sources, describe the named examples, and distinguish Archimedean solids from Platonic solids, Johnson solids, Catalan solids and prisms and antiprisms.
One of thirteen highly symmetric convex polyhedra whose faces are two or more kinds of regular polygon meeting identically at every vertex, more symmetric than the Johnson solids but less than the five Platonic solids, with examples the registry aliases name such as the truncated icosahedron, the shape of a classic football, the icosidodecahedron, the truncated dodecahedron and octahedron, and the chiral snub cube and snub dodecahedron; Archimedean solids are named after Archimedes and are studied in geometry, with duals called the Catalan solids. Counting conventions vary slightly for chiral forms.
What it is for: A class of highly symmetric semiregular polyhedra.
It can be explain the definition; relay the thirteen solids and symmetry; describe named examples; distinguish related solids.
Distinguishing features
Two or more regular polygon faces
Identical vertices
Thirteen solids
Catalan duals
What it looks like
Convex solids with faces of two or more regular polygon types, such as a football shape.
Physical character
number: 13 count - plus chiral pairs
vertices: all identical note - vertex-transitive
registry parent: convex polyhedron note
How it is recognised
Semiregular convex polyhedron with identical vertices
Truncated icosahedron, icosidodecahedron, truncated dodecahedron, snub cube, snub dodecahedron, truncated octahedron
Platonic solids have one face type; Johnson solids are less symmetric; Catalan solids are the duals; prisms and antiprisms are separate infinite families
Related models
is a kind of - in registry terms
is contrasted with -
is contrasted with -
has dual -
In practice
Families and kinds
truncated solids
cuboctahedron and icosidodecahedron
snub solids
rhombic solids
Standards and regulation
Not applicable
Failure modes and hazards
Confusing Archimedean and Platonic solids
Miscounting chiral forms
Confusing with Catalan solids
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What an Archimedean solid is.
Science.
Definition
Definition.
Definition
Definition.
- What is an Archimedean solid, and how does it differ from Platonic solids, Johnson solids, Catalan solids and prisms and antiprisms? definition
- Is the question about geometry or a specific solid? boundary
Examples
Named examples.
Examples
Examples.
- What are the truncated icosahedron, icosidodecahedron and snub cube? definition
- Which entry fits the specific solid? action
Geometry Geometry.
Science.
Symmetry
Symmetry.
Symmetry
Symmetry.
- What makes vertices identical in Archimedean solids? provenance
- Which references are standard? provenance
Construction
Truncation and snubbing.
Construction
Construction.
- How are Archimedean solids formed by truncation and snubbing? provenance
- Which sources are cited? provenance
Duals Duals.
Science.
Catalan
Catalan solids.
Catalan
Catalan.
- How do the Catalan solids relate as duals? provenance
- Which entry fits Catalan solid? action
Chiral
Chiral solids.
Chiral
Chiral.
- Why are the snub cube and snub dodecahedron chiral? provenance
- Is the information accurate? boundary
Context Uses.
Sources.
Football
Truncated icosahedron.
Football
Football.
- Why is the truncated icosahedron the classic football shape? provenance
- Which entry fits truncated icosahedron? action
History
History.
History
History.
- How are these solids linked to Archimedes and Kepler? provenance
- Is the presentation neutral and attributed? boundary
What the second pass must settle
- Should each solid be a separate entry?
- How should chiral pairs be counted?
- How should Catalan solids be linked?