Quasiprismatorhombated hexadecachoron

Quasiprismatorhombated hexadecachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Quiproh
Coxeter diagram	x4/3x3o3x ()
Elements
Cells	32 triangular prisms, 24 octagrammic prisms, 16 cuboctahedra, 8 quasitruncated hexahedra
Faces	64+64 triangles, 96+96 squares, 48 octagrams
Edges	96+192+192
Vertices	192
Vertex figure	Skewed rectangular pyramid, base edge lengths 1, √2, 1, √2; lateral edge lengths √2, √2, √2–√2, √2–√2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Stop–4–trip:
	Quith–8/3–stop: 135°
	Quith–3–co: 60°
	Co–4–stop: 45°
	Co–3–trip: 30°
Related polytopes
Army	Semi-uniform Prit, edge lengths (small rhombicuboctahedra), (sides of square prisms)
Regiment	Quiproh
Conjugate	Prismatorhombated hexadecachoron
Abstract & topological properties
Flag count	6144
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The quasiprismatorhombated hexadecachoron, or quiproh, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 24 octagrammic prisms, 16 cuboctahedra, and 8 quasitruncated hexahedra. 1 triangular prism, 2 octagrammic prisms, 1 cuboctahedron, and 1 quasitruncated hexahedron join at each vertex. It can be obtained by quasiruncitruncating the tesseract.

The quasiprismatorhombated hexadecachoron can be vertex-inscribed into a sphenoverted trisicositetrachoron. Blending 3 quasiprismatorhombated hexadecachora results in the great rhombic disicositetrachoron.

Cross-sections[edit | edit source]

The vertices of a quasiprismatorhombated hexadecachoron of edge length 1 are given by all permutations of:

$\left(\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}}\right).$

The quasiprismatorhombated hexadecachoron is the colonel of a 3-member regiment that also includes the great prismatohexadecadisoctachoron and great rhombiprismic tesseractihexadecachoron.