Hollow cubic gyrotrigonism

Hollow cubic gyrotrigonism
(OFF file)
Rank	5
Type	Scaliform
Elements
Tera	3 hollow cubic cupoliprisms 18 blends of 2 antiduowedges
Cells	72 square pyramids 36 blends of 2 triangular prisms 36 tetrahedra (as 18 stella octangulas)
Faces	144+48 triangles 72 squares
Edges	36+144
Vertices	36
Measures (edge length 1)
Circumradius	${\frac {\sqrt {6}}{3}}\approx 0.81650$
Hypervolume	$0$
Related polytopes
Army	Traco
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	B3×A2, order 288
Convex	No

This scaliform polyteron can be created as a blend of 6 tridiminished rectified hexatera.

Vertex coordinates

The vertices of a hollow cubic gyrotrigonism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm {\frac {\sqrt {2}}{4}},\,-{\frac {\sqrt {6}}{12}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,0,\,{\frac {\sqrt {6}}{6}}\right).$