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The tetragonal disphenoid tetrahedral honeycomb is a space-filling tessellation 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.
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 A3 / D3 lattice, which is also known as the body-centered cubic lattice.
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