| Set of uniform antiprismatic prisms Example square antiprismatic prism Schlegel diagram |
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| Type | Prismatic uniform polychoron |
| Schläfli symbol | s{p,2}x{} |
| Coxeter-Dynkin | |
| Cells | 2 p-gonal antiprisms, 2 p-gonal prisms and 2p triangular prisms |
| Faces | 4p {3}, 4p {4} and 4 {p} |
| Edges | 10p |
| Vertices | 4p |
| Vertex figure | irregular quadrilateral pyramid (Example for square antiprismmic prism) |
| Symmetry group | [(p,2)+,2], order 4p |
| Properties | convex if the base is convex |
(Example net for square antiprismatic prism) |
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In 4-dimensional geometry, a uniform antiprismatic prism is a uniform polychoron with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces.
A p-gonal antiprismatic prism has 4p triangle, 4p square and 4 p-gon faces. It has 10p edges, and 4p vertices.
The convex set includes:
| Name | Coxeter graph | Cells | Image |
|---|---|---|---|
| Triangular antiprismatic prism | 2 octahedras connected by 8 triangular prisms (same as the octahedral prism) | ||
| Square antiprismatic prism | 2 square antiprisms connected by 2 cubes and 8 triangular prisms | ||
| Pentagonal antiprismatic prism | 2 pentagonal antiprisms connected by 2 pentagonal prisms and 10 triangular prisms | ||
| Hexagonal antiprismatic prism | 2 hexagonal antiprisms connected by 2 hexagonal prisms and 12 triangular prisms | ||
| Heptagonal antiprismatic prism | 2 heptagonal antiprisms connected by 2 heptagonal prisms and 14 triangular prisms | ||
| Octagonal antiprismatic prism | 2 octagonal antiprisms connected by 2 octagonal prisms and 16 triangular prisms |
There are also nonconvex forms following the set of star antiprisms: