Skewverted prismatohexadecadistesseract

Skewverted prismatohexadecadistesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Kaviphdit
Coxeter diagram	x4o3x3x3/2*b ()
Elements
Cells	32 hexagonal prisms, 16 octahemioctahedra, 8 small rhombicuboctahedra, 8 quasirhombicuboctahedra
Faces	64+64 triangles, 48+96+96 squares, 64 hexagons
Edges	192+192+192
Vertices	192
Vertex figure	Crossed skewed wedge, base edge lengths 1, 1, √2; lateral edge lengths √2, √2, √3
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	${\frac {70}{3}}\approx 23.33333$
Dichoral angles	Oho–6–hip: 150°
	Querco–4–hip: $\arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }$
	Querco–3–oho: 120°
	Querco–4–sirco: 90°
	Sirco–3–oho: 60°
	Sirco–4–hip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Semi-uniform Proh, edge lengths ${\sqrt {2}}-1$ (truncated cubes), 1 (bases of triangular prisms)
Regiment	Skiviphado
Conjugate	Skewverted prismatohexadecadistesseract
Abstract & topological properties
Flag count	6912
Euler characteristic	–16
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The skewverted prismatohexadecadistesseract, or kaviphdit, is a nonconvex uniform polychoron that consists of 32 hexagonal prisms, 16 octahemioctahedra, 8 small rhombicuboctahedra, and 8 quasirhombicuboctahedra. 1 octahemioctahedron, 1 small rhombicuboctahedron, 1 quasirhombicuboctahedron, and 2 hexagonal prisms join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small skewverted prismatohexadecadisoctachoron.

External links

• Bowers, Jonathan. "Category 14: Skewverts" (#555).

• Klitzing, Richard. "kaviphdit".