Bilbirothawroid (EntityClass, 12)
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* [[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. | * [[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 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. | ||
* 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. | * 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. | ||
Revision as of 19:39, 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.
