Tetragonal disphenoid tetrahedral honeycomb | |
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Type | convex uniform honeycomb dual |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cell type | ![]() Tetragonal disphenoid |
Face types | isosceles triangle {3} |
Vertex figure | ![]() tetrakis hexahedron ![]() ![]() ![]() ![]() ![]() |
Space group | Im3m (229) |
Symmetry | [[4, 3, 4]] |
Coxeter group | , [4, 3, 4] |
Dual | Bitruncated cubic honeycomb |
Properties | cell-transitive, face-transitive, vertex-transitive |
The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of identical tetragonal disphenoidal cells. Cells are face-transitive with 4 identical isosceles triangle faces. John Horton Conway calls it an oblate tetrahedrille or shortened to obtetrahedrille.[1]
A cell can be seen as 1/12 of a translational cube, with its vertices centered on two faces and two edges. Four of its edges belong to 6 cells, and two edges belong to 4 cells.
The tetrahedral disphenoid honeycomb is the dual of the uniform bitruncated cubic honeycomb.
Its vertices form the A*
3 / D*
3 lattice, which is also known as the body-centered cubic lattice.