Triangular hebesphenorotunda pseudopyramid (EntityTopic, 14)
From Hi.gher. Space
The triangular hebesphenorotunda pseudopyramid or J92 || triangle is a non-trivial, non-orbiform monostratic CRF polychoron similar to the bilunabirotunda pseudopyramid. Its cells are one triangular hebesphenorotunda, one octahedron, three pentagonal pyramids, three square pyramids, three triangular prisms, 6+3=9 tetrahedra and one triangular cupola. Its faces are one hexagon, three pentagons, 3+3+3=9 squares and 1+3+6+3+3+6+6+6+6+3+1+3=47 triangles. It has 3+6+3+6+6+6+3+3+6+6+3+6+3=60 edges and 3+6+3+6+3=21 vertices.
Top view:
Side view:
Coordinates
J92:
→ x3o:
<0, 2∕√3, 2φ2∕√3, 0>
<±1, -1∕√3, 2φ2∕√3, 0>
→ f3x:
<±1, φ3/√3, 2φ∕√3, 0>
<±φ2, -1∕φ√3, 2φ∕√3, 0>
<±φ, -φ+2∕√3, 2φ∕√3, 0>
→ o3F:
<±φ2, φ2∕√3, 2∕√3, 0>
<0, -2φ2∕√3, 2∕√3, 0>
→ hexagonal base:
<±1, ±√3, 0, 0>
<±2, 0, 0, 0>
triangle:
→ o3x:
<0, -2∕√3, φ2∕√3, 1/φ>
<±1, 1∕√3, φ2∕√3, 1/φ>
Incidence matrix
Dual: (dual of triangular hebesphenorotunda pseudopyramid)
# | TXID | Va | Vb | Vc | Vd | Ve | Ea | Eb | Ec | Ed | Ee | Ef | Eg | Eh | Ei | Ej | Ek | El | Em | 3a | 5a | 3b | 4a | 3c | 3d | 6a | 3e | 3f | 4b | 3g | 3h | 3i | 4c | 3j | 3k | 3l | C1a | C2a | C3a | C4a | C5a | C6a | C6b | C7a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; top | |||||||||||||||||||||||||||||||||||||||||||
1 | Vb | = point | ; mid | |||||||||||||||||||||||||||||||||||||||||||
2 | Vc | = point | ; cross | |||||||||||||||||||||||||||||||||||||||||||
3 | Vd | = point | ; bot | |||||||||||||||||||||||||||||||||||||||||||
4 | Ve | = point | ; apex | |||||||||||||||||||||||||||||||||||||||||||
5 | Ea | 2 | 0 | 0 | 0 | 0 | = digon | ; top to pen | ||||||||||||||||||||||||||||||||||||||
6 | Eb | 1 | 1 | 0 | 0 | 0 | = digon | ; pen to tola | ||||||||||||||||||||||||||||||||||||||
7 | Ec | 0 | 2 | 0 | 0 | 0 | = digon | ; tola to square | ||||||||||||||||||||||||||||||||||||||
8 | Ed | 0 | 1 | 1 | 0 | 0 | = digon | ; pen to bola | ||||||||||||||||||||||||||||||||||||||
9 | Ee | 0 | 1 | 0 | 1 | 0 | = digon | ; bola to square | ||||||||||||||||||||||||||||||||||||||
10 | Ef | 0 | 0 | 1 | 1 | 0 | = digon | ; bola to lat | ||||||||||||||||||||||||||||||||||||||
11 | Eg | 0 | 0 | 0 | 2 | 0 | = digon | ; square to bot | ||||||||||||||||||||||||||||||||||||||
12 | Eh | 0 | 0 | 0 | 2 | 0 | = digon | ; lat to bot | ||||||||||||||||||||||||||||||||||||||
13 | Ei | 1 | 0 | 0 | 0 | 1 | = digon | ; top to apex | ||||||||||||||||||||||||||||||||||||||
14 | Ej | 0 | 1 | 0 | 0 | 1 | = digon | ; mid to apex | ||||||||||||||||||||||||||||||||||||||
15 | Ek | 0 | 0 | 1 | 0 | 1 | = digon | ; cross to apex | ||||||||||||||||||||||||||||||||||||||
16 | El | 0 | 0 | 0 | 1 | 1 | = digon | ; bot to apex | ||||||||||||||||||||||||||||||||||||||
17 | Em | 0 | 0 | 0 | 0 | 2 | = digon | ; roof | ||||||||||||||||||||||||||||||||||||||
18 | 3a | 3 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; top | |||||||||||||||||||||||||
19 | 5a | 2 | 2 | 1 | 0 | 0 | 1 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = pentagon | ; pen | |||||||||||||||||||||||||
20 | 3b | 1 | 2 | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; tola | |||||||||||||||||||||||||
21 | 4a | 0 | 2 | 0 | 2 | 0 | 0 | 0 | 1 | 0 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | = square | ; square | |||||||||||||||||||||||||
22 | 3c | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; bola | |||||||||||||||||||||||||
23 | 3d | 0 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | = triangle | ; lat | |||||||||||||||||||||||||
24 | 6a | 0 | 0 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | = hexagon | ; bot | |||||||||||||||||||||||||
25 | 3e | 2 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | = triangle | ; top-pen to apex | |||||||||||||||||||||||||
26 | 3f | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | = triangle | ; pen-tola to apex | |||||||||||||||||||||||||
27 | 4b | 0 | 2 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 1 | = square | ; tola-square to apex | |||||||||||||||||||||||||
28 | 3g | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | = triangle | ; pen-bola to apex | |||||||||||||||||||||||||
29 | 3h | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | = triangle | ; bola-square to apex | |||||||||||||||||||||||||
30 | 3i | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | = triangle | ; bola-lat to apex | |||||||||||||||||||||||||
31 | 4c | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 2 | 1 | = square | ; square-bot to apex | |||||||||||||||||||||||||
32 | 3j | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 2 | 0 | = triangle | ; lat-bot to apex | |||||||||||||||||||||||||
33 | 3k | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | = triangle | ; roof | |||||||||||||||||||||||||
34 | 3l | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 1 | = triangle | ; top to roof | |||||||||||||||||||||||||
35 | C1a | 3 | 6 | 3 | 6 | 0 | 3 | 6 | 3 | 6 | 6 | 6 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 3 | 3 | 6 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangular hebesphenorotunda | ; | ||||||||
36 | C2a | 3 | 0 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 | 0 | 0 | 0 | 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 3 | = octahedron | ; top to roof | ||||||||
37 | C3a | 2 | 2 | 1 | 0 | 1 | 1 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | = pentagonal pyramid | ; pen to roof | ||||||||
38 | C4a | 1 | 2 | 0 | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | = square pyramid | ; tola to roof | ||||||||
39 | C5a | 0 | 2 | 0 | 2 | 2 | 0 | 0 | 1 | 0 | 2 | 0 | 1 | 0 | 0 | 2 | 0 | 2 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 2 | 0 | 1 | 0 | 0 | 0 | = triangular prism | ; square to roof | ||||||||
40 | C6a | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | = tetrahedron | ; bola to roof | ||||||||
41 | C6b | 0 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 0 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 0 | 0 | = tetrahedron | ; lat to roof | ||||||||
42 | C7a | 0 | 0 | 0 | 6 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 6 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | 1 | 0 | = triangular cupola | ; bot to roof | ||||||||
43 | H4.1a | 3 | 6 | 3 | 6 | 3 | 3 | 6 | 3 | 6 | 6 | 6 | 3 | 3 | 6 | 6 | 3 | 6 | 3 | 1 | 3 | 3 | 3 | 6 | 3 | 1 | 3 | 6 | 3 | 6 | 6 | 6 | 3 | 3 | 1 | 3 | 1 | 1 | 3 | 3 | 3 | 6 | 3 | 1 | = triangular hebesphenorotunda pseudopyramid | ; |
Usage as facets
This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.