Stack of truncated square tiling alterprisms
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| Stack of truncated square tiling alterprisms | |
|---|---|
 | |
| Rank | 4 |
| Type | Scaliform |
| Space | Euclidean |
| Elements | |
| Cells | square cupolas tetrahedra |
| Faces | triangles squares of 2 orbits octagons |
| Edges | 3 orbits |
| Vertices | 1 orbit |
| Vertex figure | Blend of 2 trapezoidal pyramids  |
| Related polytopes | |
| Army | * |
| Regiment | * |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Convex | No |
| Nature | Tame |
This scaliform honeycomb consists of tetrahedra and square cupolas. It can be formed by blending together infinitely many truncated square tiling alterprisms at their bases.
It is notable for being concave - it does not intersect itself, but there are vertices inside the square cupolas' circumspheres, so it is not a Delone tiling. This is visible in its vertex figure.
If truncated square tiling prisms are inserted between the layers, the small rhombi-tetrahedral-octahedral honeycomb is formed.
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Vertex figure