Bilbirothawroid (EntityClass, 12)

From Hi.gher. Space

Revision as of 08:00, 5 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, bilunabirotunda, triangular hebesphenorotunda, to name a few).

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.

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