# Truncated snub demitesseract (EntityTopic, 13)

### From Hi.gher. Space

The **truncated snub demitesseract** is a CRF polychoron derived from the snub demitesseract via truncation. Its surface consists of 24 truncated icosahedra, 96 tridiminished icosahedra, and 120 truncated tetrahedra. It was discovered by Andrew Weimholt in 2004.

## Projections

Centered on a truncated icosahedron:

## Coordinates

epacs<0, 1, 3*phi, 3*phi^2> epacs<0, 2+phi, 1+3*phi, 3+2*phi> epacs<0, phi^3, phi^4, 3+phi> epacs<1, 2, 1+3*phi, phi^4> epacs<1, 2*phi, 3*phi^2, 2+phi> epacs<phi, 2, phi^3, 3*phi^2>

where phi = (1+√5)/2 is the Golden Ratio.

## Incidence matrix

Dual: (dual of truncated snub demitesseract)

# | TXID | Va | Vb | Vc | Ea | Eb | Ec | Ed | Ee | Ef | 6a | 3a | 6b | 3b | 5a | 6c | 3c | C1a | C2a | C2b | C3a | Type | Name |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | Va | = point | ; "head" of {5} | ||||||||||||||||||||

1 | Vb | = point | ; "arms" of {5} | ||||||||||||||||||||

2 | Vc | = point | ; "legs" of {5} | ||||||||||||||||||||

3 | Ea | 2 | 0 | 0 | = digon | ; | |||||||||||||||||

4 | Eb | 2 | 0 | 0 | = digon | ; | |||||||||||||||||

5 | Ec | 1 | 1 | 0 | = digon | ; | |||||||||||||||||

6 | Ed | 0 | 1 | 1 | = digon | ; | |||||||||||||||||

7 | Ee | 0 | 1 | 1 | = digon | ; | |||||||||||||||||

8 | Ef | 0 | 0 | 2 | = digon | ; | |||||||||||||||||

9 | 6a | 6 | 0 | 0 | 3 | 3 | 0 | 0 | 0 | 0 | = hexagon | ; | |||||||||||

10 | 3a | 3 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | = triangle | ; | |||||||||||

11 | 6b | 2 | 2 | 2 | 1 | 0 | 2 | 0 | 2 | 1 | = hexagon | ; | |||||||||||

12 | 3b | 2 | 1 | 0 | 0 | 1 | 2 | 0 | 0 | 0 | = triangle | ; | |||||||||||

13 | 5a | 1 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 1 | = pentagon | ; | |||||||||||

14 | 6c | 0 | 3 | 3 | 0 | 0 | 0 | 3 | 3 | 0 | = hexagon | ; | |||||||||||

15 | 3c | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 3 | = triangle | ; | |||||||||||

16 | C1a | 12 | 24 | 24 | 6 | 0 | 24 | 24 | 24 | 12 | 0 | 0 | 12 | 0 | 12 | 8 | 0 | = truncated icosahedron | ; | ||||

17 | C2a | 12 | 0 | 0 | 6 | 12 | 0 | 0 | 0 | 0 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | = truncated tetrahedron | ; full sym | ||||

18 | C2b | 6 | 3 | 3 | 3 | 3 | 6 | 0 | 3 | 3 | 1 | 0 | 3 | 3 | 0 | 0 | 1 | = truncated tetrahedron | ; axial sym | ||||

19 | C3a | 3 | 3 | 3 | 0 | 3 | 6 | 3 | 0 | 3 | 0 | 1 | 0 | 3 | 3 | 0 | 1 | = tridiminished icosahedron | ; | ||||

20 | H4.1a | 288 | 288 | 288 | 144 | 288 | 576 | 288 | 288 | 288 | 96 | 96 | 288 | 288 | 288 | 96 | 96 | 24 | 24 | 96 | 96 | = truncated snub demitesseract |
; |

## Usage as facets

*This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.*