Bilbirothawroid (EntityClass, 12)
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* 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 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 [[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 pyramid]]s. It also has a [[Stott-expanded]] variant, first suggested by [[student91]], consisting of two parallel [[rhodopantohedra]], 30 bilunabirotundae, 40 [[triangular prism]]s, 24 [[pentagonal cupola]]e, and 72 [[pentagonal prism]]s. | * 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 pyramid]]s. It also has a [[Stott-expanded]] variant, first suggested by [[student91]], consisting of two parallel [[rhodopantohedra]], 30 bilunabirotundae, 40 [[triangular prism]]s, 24 [[pentagonal cupola]]e, and 72 [[pentagonal prism]]s. | ||
| - | * The [[triangular hebesphenorotundaeic rhombochoron]] (or J92-rhombochoron), containing four | + | * The [[triangular hebesphenorotundaeic rhombochoron]] (or J92-rhombochoron), containing four triangular hebesphenorotundae (J92) cells at a 60°/120° dichoral angles to each other, 6 metabidiminished icosahedra (J62), 6 triangular prisms, 24 pentagonal pyramids, 30 square pyramids, and 12 tetrahedra, discovered by [[Quickfur]] on February 6, 2014 based on a suggestion given by student91 after a previous failed attempt to construct a CRF with J92 cells. |
Revision as of 22:49, 10 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),
- 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 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.
- The triangular hebesphenorotundaeic rhombochoron (or J92-rhombochoron), containing four triangular hebesphenorotundae (J92) cells at a 60°/120° dichoral angles to each other, 6 metabidiminished icosahedra (J62), 6 triangular prisms, 24 pentagonal pyramids, 30 square pyramids, and 12 tetrahedra, discovered by Quickfur on February 6, 2014 based on a suggestion given by student91 after a previous failed attempt to construct a CRF with J92 cells.
