Tesseractic tetracomb
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| Tesseractic tetracomb | |
|---|---|
 Perspective projection of a 3x3x3x3 red-blue chessboard. |
|
| Type | Regular tetracomb |
| Schläfli symbol | {4,3,3,4} |
| Coxeter-Dynkin diagram |     |
| Hypercell type | {4,3,3} |
| Cell type | {4,3} |
| Face type | {4} |
| Edge figure | 8 {4,3} (octahedron) |
| Vertex figure | 8 {4,3,3} (16-cell) |
| Coxeter group | [4,3,3,4] |
| Dual | self-dual |
| Properties | vertex-transitive, edge-transitive, face-transitive, cell-transitive |
The tesseractic tetracomb is the one of three regular space-filling tessellation (or honeycomb) in Euclidean 4-space. Four tesseracts meet at each each face, and it is more explicitly called an order-4 tesseractic tetracomb.
It is an analog of the square tiling of the plane and the cubic honeycomb of 3-space.
There is also an order-5 tesseractic tetracomb, {4,3,3,5}, that can be constructed on a hyperbolic 4-space.
It is also related to the regular penteract which exists in 5-space with 3 tesseracts on each face. This could equivalently be considered an order-3 tesseractic tetracomb, {4,3,3,3}, on the 4-sphere.
[edit] See also
[edit] References
- Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table II: Regular honeycombs
- George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)
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