Crown jewel (EntityClass, 11)
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(moved Crown jewel to Bilbirothawroid: The bulk of this article is specific to BT polytopes - will recreate for crown jewels in general.) |
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| - | # | + | <[#ontology [kind class] [cats CRF Polytope]]> |
| + | '''Crown jewels''' are a catch-all term for unusual [[Polytope#Convex_regular-faced_polytope|CRF polytope]]s 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 solid]]s at the end of Johnson's list: | ||
| + | * [[Snub disphenoid]] (J84), | ||
| + | * [[Snub square antiprism]] (J85), | ||
| + | * [[Sphenocorona]] (J86), | ||
| + | * [[Augmented sphenocorona]] (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 [[ursatope|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 [[bilbirothawroid]]s: a collection of polytopes containing bilbiro (J91) and/or thawro (J92) elements. | ||
Latest revision as of 15:26, 1 March 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),
- Augmented sphenocorona (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 bilbirothawroids: a collection of polytopes containing bilbiro (J91) and/or thawro (J92) elements.
