Bilbirothawroid (EntityClass, 12)

|CJ4.1||[[snubdis antiprism]]||2001? by [[Klitzing]]||The [[cube]] {{!!}} [[icosahedron]] was 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, and is the only crown jewel that is also a segmentotope.

|CJ4.2.x||[[ursatope|ursachora]]||? by [[Wendy]]||Other than the icosahedral ursachoron, the ursatopes 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]]).

|CJ4.3.1||[[castellated rhodoperihedral prism]]||February 4, 2014 by [[Quickfur]]||An unusual prism-like CRF consisting of two parallel [[rhodoperihedra]] sandwiching 30 bilunabirotundae, 40 [[tetrahedra]], and 24 [[pentagonal pyramid]]s.

|CJ4.3.2||[[castellated rhodopantohedral prism]]||[[student91]]||A [[Stott-expanded]] variant of CJ4.3.1 consisting of two parallel [[rhodopantohedra]], 30 bilunabirotundae, 40 [[triangular prism]]s, 24 [[pentagonal cupola]]e, and 72 [[pentagonal prism]]s.

|CJ4.4||[[triangular hebesphenorotundaeic rhombochoron]] (or J92-rhombochoron)||February 6, 2014 by Quickfur||Contains four triangular hebesphenorotundae (J92) cells at 60° and 120° dichoral angles to each other, 6 metabidiminished icosahedra (J62), 6 triangular prisms, 24 pentagonal pyramids, 30 square pyramids, and 12 tetrahedra. Based on a suggestion given by [[student91]] after a previous failed attempt to construct a CRF with J92 cells.

|[[CJ4.5.1]]||diminished triacontasphenorotunda (tentative name)||February 13, 2014 by [[student91]] and [[Klitzing]]||Based on an idea by [[Quickfur]] that a CRF with J92 cells might exist as a modified diminishing of the rectified 120-cell. Has 30 tetrahedra, 60 square pyramids, 30 triangular prisms, 12 pentagonal cupolae, 12 [[pentagonal rotunda]]e, 1 rhodopantohedron, 1 [[truncated dodecahedron]], and 20 [[triangular hebesphenorotunda|J92]]'s, for a total of 166 cells.  

|CJ4.5.2||triacontasphenorotunda (tentative name)||February 13, 2014 by student91||Discovered at the same time as CJ4.5.1, the non-diminished form has 70 tets + 20 J92's + 13 ids + 12 pecues + 60 squippies + 30 trips + 1 grid.

|[[CJ4.5.3]]||''none yet''||February 15, 2014 by Quickfur||A related CRF constructed from the remainder of the rectified 120-cell after the above modified diminishing, which contains 40 J92's, 24 [[decagonal prism]]s, 24 pentagonal rotundae, 180 square pyramids, 220 tetrahedra, 30 [[rhodomesohedra]], and two rhodopantohedra.

|[[CJ4.5.4]]||''none yet''||February 15, 2014 by [[Marek14]]||A "squashed" version of the previous CRF, in which the 30 rhodomesohedra are replaced with bilunabirotundae (J91). This was confirmed to be CRF by Quickfur. It has 2 rhodopantohedra, 40 J92's, 30 J91's, 36 decagonal prisms, and 240 square pyramids. It is the first known crown jewel that contains two 3D crown jewels as cells, the bilunabirotunda (J91), and the triangular hebesphenorotunda (J92).

|[[CJ4.6]]||''none yet''||February 18, 2014 by student91||A CRF containing 30 [[bilunabirotunda|J91]] cells derived from the [[hydrocantichoron]] o5x3o3x. This CRF was successfully constructed by [[Quickfur]] on February 20, 2014 and verified to be CRF.

|[[CJ4.7]]||''none yet''||February 24, 2014 by student91||An octa-diminishing of a modified rectified 600-cell (diminished) tristratic cap, containing 8 [[triangular hebesphenorotunda|J92]] lacing an icosidodecahedron and a truncated icosahedron on parallel hyperplanes.

|[[CJ4.8]]||''none yet''||February 25, 2014 by Quickfur||A CRF made from a tetrahedron-centered patch of the rectified 120-cell's surface, with modifications that create 4 [[triangular hebesphenorotunda|J92]] cells, 4 [[bilunabirotunda|J91]] cells, 4 [[tridiminished icosahedra]] (J63), and an assortment of other cells.

|[[CJ4.8.2]]||''none yet''||February 26, 2014 by [[student5]]||A related CRF made from a truncated tetrahedron surrounded by four [[triangular hebesphenorotunda|J92]]'s (joined at the hexagonal faces), and attached to the same configuration of 1+4 octahedra and 4 [[bilunabirotunda|J91]]'s on the other side, just like CJ4.8.

|[[CJ4.9.0]]||''none yet''||[http://hddb.teamikaria.com/forum/viewtopic.php?f=25&t=1468&p=20554&hilit=+relpaced#p20554 February 22, 2014] by student91||A compressed rectified 600-cell, wherein the vertex layers of the latter between two embedded truncated dodecahedra are deleted and the rest of the polytope compressed together. Parent of a family of related CRFs. For the further CRF's, you delete one or more decagon-decagon edges of the truncated dodecahedron to create [[bilunabirotunda|J91]] cells.

|[[CJ4.9.1]]||''none yet''||February 22 2014, by student91||One of the family described above. It is constructed by deleting the decagon-decagon edges such that the resulting polytope gets pyritohedral symmetry.

|[[CJ4.9.2]]||''none yet''||February 22 2014, by student91||Another one of the family described above. this one has it's decagon-decagon edges deleted in a way that produces pentagonal antiprismatic symmetry. This is the maximal possible diminishing of decagon-decagon edges.