| Triakis truncated tetrahedral honeycomb | |
|---|---|
| |
| Cell type | Triakis truncated tetrahedron |
| Face types | hexagon isosceles triangle |
| Coxeter group | Ã3×2, ] (double) |
| Space group | Fd3m (227) |
| Properties | Cell-transitive |
The triakis truncated tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of triakis truncated tetrahedra. It was discovered in 1914.
Voronoi tessellation
It is the Voronoi tessellation of the carbon atoms in diamond, which lie in the diamond cubic crystal structure.
Being composed entirely of triakis truncated tetrahedra, it is cell-transitive.
Relation to quarter cubic honeycomb
It can be seen as the uniform quarter cubic honeycomb where its tetrahedral cells are subdivided by the center point into 4 shorter tetrahedra, and each adjoined to the adjacent truncated tetrahedral cells.
See also
References
- Föppl, L. (1914). "Der Fundamentalbereich des Diamantgitters". Phys. Z. 15: 191–193.
- Grünbaum, B.; Shephard, G. C. (1980). "Tilings with Congruent Tiles". Bull. Amer. Math. Soc. 3 (3): 951–973. doi:10.1090/s0273-0979-1980-14827-2.
- Conway, John. "Voronoi Polyhedron". geometry.puzzles. Retrieved 20 September 2012.
- Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008). The Symmetries of Things. p. 332. ISBN 978-1568812205.
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