Bilbirothawroid (EntityClass, 12)
From Hi.gher. Space
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== 3D == | == 3D == | ||
| - | They are the unusual [[Johnson solid]]s at the end of Johnson's list | + | They are the unusual [[Johnson solid]]s at the end of Johnson's list: |
| + | * [[Snub disphenoid]] (J84), | ||
| + | * [[Snub square antiprism]] (J85), | ||
| + | * [[Sphenocorona]] (J86) and its augmented variant J87, | ||
| + | * [[Sphenomegacorona]] (J88), | ||
| + | * [[Hebesphenomegacorona]] (J89), | ||
| + | * [[Disphenocingulum]] (J90), | ||
| + | * [[Bilunabirotunda]] (J91), | ||
| + | * [[Triangular hebesphenorotunda]] (J92). | ||
== 4D == | == 4D == | ||
Revision as of 19:32, 6 February 2014
Crown jewels are a catch-all term for unusual CRF polytopes with unique structures that cannot be obtained from the uniform polytopes or other simpler CRFs by simple "cut-and-paste" operations.
3D
They are the unusual Johnson solids at the end of Johnson's list:
- Snub disphenoid (J84),
- Snub square antiprism (J85),
- Sphenocorona (J86) and its augmented variant J87,
- Sphenomegacorona (J88),
- Hebesphenomegacorona (J89),
- Disphenocingulum (J90),
- Bilunabirotunda (J91),
- Triangular hebesphenorotunda (J92).
4D
So far, the following crown jewels have been discovered:
- snubdis antiprism (cube || icosahedron): a crown jewel discovered by Klitzing and included in his list of segmentochora. It is considered a crown jewel because it involves the non-obvious placement of two polyhedra of different symmetry groups in parallel hyperplanes.
- The non-icosahedral ursachora are arguably crown jewels as well, since they cannot be derived from the uniform polychora by simple "cut-and-paste" operations, and their construction was non-obvious until Wendy first constructed the icosahedral variant (which happens to be a diminishing of the hydrochoron).
- The castellated rhodoperihedral prism: an unusual prism-like CRF discovered by Quickfur on February 4, 2014, consisting of two parallel rhodoperihedra sandwiching 30 bilunabirotundae, 40 tetrahedra, and 24 pentagonal pyramids. It also has a Stott-expanded variant, first suggested by student91, consisting of two parallel rhodopantohedra, 30 bilunabirotundae, 40 triangular prisms, 24 pentagonal cupolae, and 72 pentagonal prisms.
- An unusual hydrochoron luna that contains two triangular hebesphenocorona (J92) cells at a 60° dichoral angle to each other, incompletely constructed by Quickfur on February 5, 2014, and completed by Klitzing the following day. A 120° variant is conjectured to exist, though it has not been proven yet.
