Where " V " is the volume of the disphenoid and " T " is the area of any face, which is given by Heron's formula.
12.
John Horton Conway calls this honeycomb a "'truncated octahedrille "'in his Architectonic and catoptric tessellation list, with its dual called an " oblate tetrahedrille ", also called a disphenoid tetrahedral honeycomb.
13.
This definition is used in the naming two Johnson solids : snub disphenoid, and snub square antiprism, as well as higher dimensional polytopes such as the 4-dimensional snub 24-cell, or s { 3, 4, 3 }.
14.
There are no well-covered 5-connected maximal planar graphs, and there are only four 4-connected well-covered maximal planar graphs : the graphs of the regular octahedron, the pentagonal dipyramid, the snub disphenoid, and an irregular polyhedron ( a nonconvex deltahedron ) with 12 vertices, 30 edges, and 20 triangular faces.
15.
An orientation of the tetragonal disphenoid honeycomb can be obtained by starting with a cubic honeycomb, subdividing it at the planes x = y, x = z, and y = z ( i . e . subdividing each cube into path-tetrahedra ), then squashing it along the main diagonal until the distance between the points ( 0, 0, 0 ) and ( 1, 1, 1 ) becomes the same as the distance between the points ( 0, 0, 0 ) and ( 0, 0, 1 ).
