Triangulated pinched triangular cupola (EntityTopic, 13)
From Hi.gher. Space
The triangulated pinched triangular cupola is one of the non-CRF facets of CRF duals currently being studied by Keiji. It is self-dual and chiral, and in fact has no symmetry at all.
Trivia
The color names in the imat below correspond to the following diagram:
This coloring made it possible to find a valid permutation without having to brute force search through 8! * 14! * 8! possibilities.
Incidence matrix
Dual: Self-dual
| # | TXID | Va | Vb | Vc | Vd | Ve | Vf | Vg | Vh | Ea | Eb | Ec | Ed | Ee | Ef | Eg | Eh | Ei | Ej | Ek | El | Em | En | 3a | 3b | 3c | 3d | 3e | 4a | 4b | 5a | Type | Name |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Va | = point | ; white | ||||||||||||||||||||||||||||||
| 1 | Vb | = point | ; red | ||||||||||||||||||||||||||||||
| 2 | Vc | = point | ; orange | ||||||||||||||||||||||||||||||
| 3 | Vd | = point | ; lime | ||||||||||||||||||||||||||||||
| 4 | Ve | = point | ; green | ||||||||||||||||||||||||||||||
| 5 | Vf | = point | ; cyan | ||||||||||||||||||||||||||||||
| 6 | Vg | = point | ; blue | ||||||||||||||||||||||||||||||
| 7 | Vh | = point | ; pink | ||||||||||||||||||||||||||||||
| 8 | Ea | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | = digon | ; wr !cp | ||||||||||||||||||||||
| 9 | Eb | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | = digon | ; wo !gc | ||||||||||||||||||||||
| 10 | Ec | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | = digon | ; wl !lg | ||||||||||||||||||||||
| 11 | Ed | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | = digon | ; wg !ol | ||||||||||||||||||||||
| 12 | Ee | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | = digon | ; wb !op | ||||||||||||||||||||||
| 13 | Ef | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | = digon | ; ro !cb | ||||||||||||||||||||||
| 14 | Eg | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | = digon | ; rb !rp | ||||||||||||||||||||||
| 15 | Eh | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | = digon | ; rp !rb | ||||||||||||||||||||||
| 16 | Ei | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | = digon | ; cb !ro | ||||||||||||||||||||||
| 17 | Ej | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | = digon | ; op !wb | ||||||||||||||||||||||
| 18 | Ek | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | = digon | ; ol !wg | ||||||||||||||||||||||
| 19 | El | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | = digon | ; lg !wl | ||||||||||||||||||||||
| 20 | Em | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | = digon | ; gc !wo | ||||||||||||||||||||||
| 21 | En | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | = digon | ; cp !wr | ||||||||||||||||||||||
| 22 | 3a | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; pink | ||||||||
| 23 | 3b | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | = triangle | ; blue | ||||||||
| 24 | 3c | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; cyan | ||||||||
| 25 | 3d | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | = triangle | ; green | ||||||||
| 26 | 3e | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | = triangle | ; lime | ||||||||
| 27 | 4a | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | = square | ; orange | ||||||||
| 28 | 4b | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | = square | ; red | ||||||||
| 29 | 5a | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | = pentagon | ; white | ||||||||
| 30 | C1a | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | = triangulated pinched triangular cupola | ; |
Usage as facets
- 24× 1-facets of a (dual of triangular hebesphenorotundaeic rhombochoron)
