Triangular hebesphenorotunda (EntityTopic, 14)
From Hi.gher. Space
The triangular hebesphenorotunda is the 92nd Johnson solid, J92.
Coordinates
The following coordinates describe a triangular hebesphenorotunda with edge length 2, with its 3-fold axis of symmetry aligned to the Z axis:
- The top triangle:
- <0, 2/√3, 2*φ^2/√3>
- <±1, -1/√3, 2*φ^2/√3>
- The base of the triangles surrounding the top triangle:
- <±1, φ^3/√3, 2*φ/√3>
- <±φ^2, -1/(φ*√3), 2*φ/√3>
- <±φ, -(φ+2)/√3, 2*φ/√3>
- The tips of the pentagons:
- <±φ^2, φ^2/√3, 2/√3>
- <0, -2*φ^2/√3, 2/√3>
- The hexagonal base
- <±1, ±√3, 0>
- <±2, 0, 0>
where φ=(1+√5)/2 is the Golden Ratio.
Incidence matrix
Dual: J92 dual
# | TXID | Va | Vb | Vc | Vd | Ea | Eb | Ec | Ed | Ee | Ef | Eg | Eh | 3a | 5a | 3b | 4a | 3c | 3d | 6a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | Va | = point | ; top | |||||||||||||||||||
1 | Vb | = point | ; mid | |||||||||||||||||||
2 | Vc | = point | ; cross | |||||||||||||||||||
3 | Vd | = point | ; bot | |||||||||||||||||||
4 | Ea | 2 | 0 | 0 | 0 | = digon | ; top to pen | |||||||||||||||
5 | Eb | 1 | 1 | 0 | 0 | = digon | ; pen to tola | |||||||||||||||
6 | Ec | 0 | 2 | 0 | 0 | = digon | ; tola to square | |||||||||||||||
7 | Ed | 0 | 1 | 1 | 0 | = digon | ; pen to bola | |||||||||||||||
8 | Ee | 0 | 1 | 0 | 1 | = digon | ; bola to square | |||||||||||||||
9 | Ef | 0 | 0 | 1 | 1 | = digon | ; bola to lat | |||||||||||||||
10 | Eg | 0 | 0 | 0 | 2 | = digon | ; square to bot | |||||||||||||||
11 | Eh | 0 | 0 | 0 | 2 | = digon | ; lat to bot | |||||||||||||||
12 | 3a | 3 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | = triangle | ; top | |||||||
13 | 5a | 2 | 2 | 1 | 0 | 1 | 2 | 0 | 2 | 0 | 0 | 0 | 0 | = pentagon | ; pen | |||||||
14 | 3b | 1 | 2 | 0 | 0 | 0 | 2 | 1 | 0 | 0 | 0 | 0 | 0 | = triangle | ; tola | |||||||
15 | 4a | 0 | 2 | 0 | 2 | 0 | 0 | 1 | 0 | 2 | 0 | 1 | 0 | = square | ; square | |||||||
16 | 3c | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | = triangle | ; bola | |||||||
17 | 3d | 0 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | = triangle | ; lat | |||||||
18 | 6a | 0 | 0 | 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 | = hexagon | ; bot | |||||||
19 | C1a | 3 | 6 | 3 | 6 | 3 | 6 | 3 | 6 | 6 | 6 | 3 | 3 | 1 | 3 | 3 | 3 | 6 | 3 | 1 | = triangular hebesphenorotunda | ; |
Usage as facets
- 1× 1-facets of a triangular hebesphenorotunda pseudopyramid
- 4× 1-facets of a triangular hebesphenorotundaeic rhombochoron
- 8× 1-facets of a D4.7
Notable Trishapes | |
Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
Snubs: | snub staurohedron • snub rhodohedron |
Curved: | sphere • torus • cylinder • cone • frustum • crind |