Truncated square antiprism
# Truncated square antiprism

Truncated square antiprism :

| Type | Truncated antiprism |
| - | - |
| Schläfli symbol | ts{2,8} tsr{4,2} or $ts{\begin{Bmatrix}4\\2\end{Bmatrix}}$ |
| Conway notation | tA4 |
| Faces | 18: 2 {8}, 8 {6}, 8 {4} |
| Edges | 48 |
| Vertices | 32 |
| Symmetry group | $D_{4d},$ $[2^+,8],$ (2*4), order 16 |
| Rotation group | $D_4,$ $[2,4]^+,$ (224), order 8 |
| Dual polyhedron | |
| Properties | convex, zonohedron |

The truncated square antiprism one in an infinite series of truncated antiprisms, constructed as a truncated square antiprism. It has 18 faces, 2 octagons, 8 hexagons, and 8 squares.

## Gyroelongated triamond square bicupola

If the hexagons are folded, it can be constructed by regular polygons. Or each folded hexagon can be replaced by two triamonds, adding 8 edges (56), and 4 faces (32). This form is called a gyroelongated triamond square bicupola.

## Related polyhedra

Truncated antiprisms :

| Symmetry | $D_{2d},$ $[2^+,4],$ (2*2) | $D_{3d},$ $[2^+,6],$ (2*3) | $D_{4d},$ $[2^+,8],$ (2*4) | $D_{5d},$ $[2^+,10],$ (2*5) |
| - | - | - | - | - |
| Antiprisms | s{2,4} (v:4; e:8; f:6) | s{2,6} (v:6; e:12; f:8) | s{2,8} (v:8; e:16; f:10) | s{2,10} (v:10; e:20; f:12) |
| Truncated antiprisms | ts{2,4} (v:16;e:24;f:10) | ts{2,6} (v:24; e:36; f:14) | ts{2,8} (v:32; e:48; f:18) | ts{2,10} (v:40; e:60; f:22) |

### Snub square antiprism

Although it can't be made by all regular planar faces, its alternation is the Johnson solid, the snub square antiprism.

