# Bilbirothawroid (EntityClass, 12)

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(Redirected from BT polychora)

A **bilbirothawroid**, **bilbiro/thawro polytope** or **BT polytope** is a crown jewel CRF polytope of at least four dimensions containing bilbiro and/or thawro elements.

Index | Name | Discovered | Description |
---|---|---|---|

D4.3.1 | 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 pyramids. |

D4.3.2 | castellated rhodopantohedral prism | student91 | A Stott-expanded variant of D4.3.1 consisting of two parallel rhodopantohedra, 30 bilunabirotundae, 40 triangular prisms, 24 pentagonal cupolae, and 72 pentagonal prisms. |

D4.4 | 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 |

D4.4.1 | tetraaugmented triangular hebesphenorotundaeic rhombochoron | March 21, 2014 by Quickfur | Augmented form of D4.4. |

D4.4.2 | none yet | March 23, 2014 by student91 | Diminishing of D4.4.1, such that six bilbiro's and two thawro's occur. It's structure was determined by Quickfur. |

D4.5.1 | 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 rotundae, 1 rhodopantohedron, 1 truncated dodecahedron, and 20 J92's, for a total of 166 cells. |

D4.5.2 | triacontasphenorotunda (tentative name) | February 13, 2014 by student91 | Discovered at the same time as D4.5.1, the non-diminished form has 70 tets + 20 J92's + 13 ids + 12 pecues + 60 squippies + 30 trips + 1 grid. |

D4.5.3 | 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 prisms, 24 pentagonal rotundae, 180 square pyramids, 220 tetrahedra, 30 rhodomesohedra, and two rhodopantohedra. |

D4.5.4 | 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). |

D4.6 | none yet | February 18, 2014 by student91 | A CRF containing 30 J91 cells derived from the hydrocantichoron o5x3o3x. This CRF was successfully constructed by Quickfur on February 20, 2014 and verified to be CRF. |

D4.7 | none yet | February 24, 2014 by student91 | An octa-diminishing of a modified rectified 600-cell (diminished) tristratic cap, containing 8 J92 lacing an icosidodecahedron and a truncated icosahedron on parallel hyperplanes. |

D4.8.1D4.8.x | 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 J92 cells, 4 J91 cells, 4 tridiminished icosahedra (J63), and an assortment of other cells. |

D4.8.2 | none yet | February 26, 2014 by student5 | A related CRF made from a truncated tetrahedron surrounded by four J92's (joined at the hexagonal faces), and attached to the same configuration of 1+4 octahedra and 4 J91's on the other side, just like D4.8. |

D4.8.3 | none yet | March 9, 2014 by student91 | A related CRF to D4.8, where the configuration of 4 J91 cells is replaced by 4 J92's surrounding an octahedron, with the gaps filled by 4 tridiminished icosahedra (J63) and some number of square pyramids and pentagonal pyramids. |

D4.8.4 | none yet | March 10, 2014 by Quickfur | A CRF formed by joining together the halves of D4.8.2 and D4.8.3 that aren't present in D4.8.1 at their skew polyhedron ends. |

D4.9.0 | none yet | 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 J91 cells. |

D4.9.1 | 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. |

D4.9.2 | 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. |

D4.10 | none yet | March 11 2014, by Quickfur | A CRF with tetrahedral symmetry, 12 J91's surrounding a pair of antipodal tetrahedra, and 8 J92's, having an arrangement approximating 16-cell symmetry. |