# Prismatorhombated demitesseract

Prismatorhombated demitesseract
Rank4
TypeSemi-uniform
SpaceSpherical
Notation
Coxeter diagramx3o3y *b3z
Elements
Cells24 cuboids, 8+8+8 rhombitetratetrahedra
Faces32+32+32 triangles, 48+48+48 rectangles
Edges96+96+96
Vertices96
Vertex figureSkewed wedge
Measures (edge lengths a, b, c)
Circumradius${\displaystyle \sqrt{\frac{a^2+b^2+c^2+ab+ac+bc}{2}}}$
Dichoral anglesRatet–4–cuboid: 135°
Ratet–3–ratet: 120°
Central density1
Related polytopes
DualSkewed notched enneacontihexachoron
ConjugatePrismatorhombated demitesseract
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryD4, order 192
ConvexYes
NatureTame

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.

## Vertex coordinates

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

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