Retrosphenoverted hexadecatesseractioctachoron

Retrosphenoverted hexadecatesseractioctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Rawvhitto
Coxeter diagram	o4x3x3/2o3*b ()
Elements
Cells	8 cuboctahedra, 16 octahemioctahedra, 8 truncated octahedra
Faces	32+64 triangles, 48 squares, 64 hexagons
Edges	96+192
Vertices	96
Vertex figure	Crossed wedge, edge lengths 1 (2 edges of base rectangle and top edge), √2 (remaining base edges), and √3 (side edges)
Measures (edge length 1)
Circumradius	$\sqrt3 ≈ 1.73205$
Hypervolume	$\frac{68}{3} ≈ 22.66667$
Dichoral angles	Oho–3–co: 120°
	Oho–3–oho: 120°
	Co–4–toe: 90°
	Oho–6–toe: 60°
Related polytopes
Army	Rico
Regiment	Rico
Conjugate	None
Convex core	Tesseract
Abstract properties
Euler characteristic	–16
Topological properties
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The retrosphenoverted hexadecatesseractioctachoron, or rawvhitto, is a nonconvex uniform polychoron that consists of 8 cuboctahedra, 8 truncated octahedra, and 16 octahemioctahedra. 1 cuboctahedron, 2 truncated octahedra, and 2 octahemioctahedra join at each vertex.

Representations

The retrosphenoverted hexadecatesseractioctachoron has the following Coxeter diagrams:

• o4x3x3/2o3*b (full symmetry)
• x3x3o3x3*a3/2*c (D₄ symmetry, skewvert)

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#147).

• Klitzing, Richard. "rawvhitto".