Small prismatohexadecadisoctachoron

Small prismatohexadecadisoctachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Siphado
Coxeter diagram	x4x3x3/2o3*b ()
Elements
Cells	32 triangular prisms, 16 octahemioctahedra, 8 truncated cubes, 8 great rhombicuboctahedra
Faces	64+64 triangles, 96 squares, 64 hexagons, 48 octagons
Edges	96+192+192
Vertices	192
Vertex figure	Skewed bowtie pyramid, base edge lengths 1, √3, 1, √3; lateral edge lengths √2, √2, √2+√2, √2+√2
Measures (edge length 1)
Circumradius	${\sqrt {4+2{\sqrt {2}}}}\approx 2.61313$
Hypervolume	$4{\frac {59+44{\sqrt {2}}}{3}}\approx 161.63386$
Dichoral angles	Oho–3–trip: 150°
	Oho–3–tic: 120°
	Tic–8–girco: 90°
	Oho–6–girco: 60°
	Girco–4–trip: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Related polytopes
Army	Proh
Regiment	Proh
Conjugate	Great prismatohexadecadisoctachoron
Abstract & topological properties
Flag count	6144
Euler characteristic	–16
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The small prismatohexadecadisoctachoron, or siphado, is a nonconvex uniform polychoron that consists of 32 triangular prisms, 16 octahemioctahedra, 8 truncated cubes, and 8 great rhombicuboctahedra. 1 triangular prism, 1 truncated cube, 1 octahemioctahedron, and 2 great rhombicuboctahedra join at each vertex.

3 copies of this polychoron can blend to form the small pseudorhombic disicositetrachoron, with the octahemioctahedron cells blending out.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the prismatorhombated hexadecachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#359).

• Klitzing, Richard. "siphado".