Runcinated tesseractic honeycomb
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| Runcinated tesseractic honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform 4-honeycomb |
| Schläfli symbol | t0,3{4,3,3,4} t0,3{4,3,31,1} |
| Coxeter-Dynkin diagram | |
| 4-face type | runcinated tesseract tesseract rectified tesseract cuboctahedral prism |
| Cell type | Cuboctahedron Tetrahedron Cube Triangular prism |
| Face type | {3}, {4} |
| Vertex figure | triangular-antipodial antifastigium |
| Coxeter group | = [4,3,3,4] = [4,3,31,1] |
| Dual | |
| Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the runcinated tesseractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 4-space. It is constructed by a runcination of a tesseractic honeycomb creating runcinated tesseracts, and new tesseract, rectified tesseract and cuboctahedral prism facets.
The [4,3,3,4], ![]()
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, Coxeter group generates 31 permutations of uniform tessellations, 21 with distinct symmetry and 20 with distinct geometry. The expanded tesseractic honeycomb (also known as the stericated tesseractic honeycomb) is geometrically identical to the tesseractic honeycomb. Three of the symmetric honeycombs are shared in the [3,4,3,3] family. Two alternations (13) and (17), and the quarter tesseractic (2) are repeated in other families.
| C4 honeycombs | |||
|---|---|---|---|
| Extended symmetry |
Extended diagram |
Order | Honeycombs |
| [4,3,3,4]: | ×1 | ||
| [[4,3,3,4]] | ×2 | ||
| [(3,3)[1+,4,3,3,4,1+]] ↔ [(3,3)[31,1,1,1]] ↔ [3,4,3,3] |
↔ ↔ |
×6 | |