Not to be confused with truncated triakis tetrahedron.
Space-filling polyhedron with 16 faces
Triakis truncated tetrahedron
Type
Plesiohedron
Faces
4 hexagons 12 isosceles triangles
Edges
30
Vertices
16
Conway notation
k3tT
Dual polyhedron
16|Order-3 truncated triakis tetrahedron
Properties
convex
In geometry, the triakis truncated tetrahedron is a convex polyhedron made from 4 hexagons and 12 isosceles triangles. It can be used to tessellate three-dimensional space, making the triakis truncated tetrahedral honeycomb.[1][2]
The triakis truncated tetrahedron is the shape of the Voronoi cell of the carbon atoms in diamond, which lie on the diamond cubic crystal structure.[3][4] As the Voronoi cell of a symmetric space pattern, it is a plesiohedron.[5]
^Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008). The Symmetries of Things. p. 332. ISBN 978-1568812205.
^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.
^Föppl, L. (1914). "Der Fundamentalbereich des Diamantgitters". Phys. Z. 15: 191–193.
^Conway, John. "Voronoi Polyhedron". geometry.puzzles. Retrieved 20 September 2012.
^Grünbaum, Branko; Shephard, G. C. (1980), "Tilings with congruent tiles", Bulletin of the American Mathematical Society, New Series, 3 (3): 951–973, doi:10.1090/S0273-0979-1980-14827-2, MR 0585178.
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