Prismatorhombated demitesseract

The prismatorhombated demitesseract is a convex semi-uniform polychoron that is a variant of the rectified icositetrachoron with demitesseractic symmetry. As such it can be represented by x3o3y *b3z, and has 24 rhombitetratetrahedra (of three types, forms x3o3y, x3o3z, and y3o3z) and 24 cuboids (type x y z) as cells, with 3 edge lengths.

Prismatorhombated demitesseract
Rank	4
Type	Semi-uniform
Space	Spherical
Notation
Coxeter diagram	x3o3y *b3z
Elements
Cells	24 cuboids, 8+8+8 rhombitetratetrahedra
Faces	32+32+32 triangles, 48+48+48 rectangles
Edges	96+96+96
Vertices	96
Vertex figure	Skewed wedge
Measures (edge lengths a, b, c)
Circumradius	$\sqrt{\frac{a^2+b^2+c^2+ab+ac+bc}{2}}$
Dichoral angles	Ratet–4–cuboid: 135°
	Ratet–3–ratet: 120°
Central density	1
Related polytopes
Dual	Skewed notched enneacontihexachoron
Conjugate	Prismatorhombated demitesseract
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	D4, order 192
Convex	Yes
Nature	Tame

Vertex coordinates

A prismatorhombated demitesseract with edge lengths a, b, and c has vertices given by all permutations and even sign changes of:

• $\left((a+2b+c)\frac{\sqrt2}{4},\,(a+c)\frac{\sqrt2}{4},\,(a+c)\frac{\sqrt2}{4},\,(a-c)\frac{\sqrt2}{4}\right).$