# Truncated snub demitesseract (EntityTopic, 13)

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

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