Decahemidecachoron

Decahemidecachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Duhd
Coxeter diagram	o3o3x3x3/2*b ()
Elements
Cells	10 tetrahedra, 5 octahemioctahedra
Faces	40 triangles, 10 hexagons
Edges	60
Vertices	20
Vertex figure	Crossed triangular prism, edge lengths 1 (base) and √3 (sides)
Edge figure	tet 3 oho 6 oho 3
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {5{\sqrt {5}}}{48}}\approx 0.23292$
Dichoral angles	Tet–3–oho: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Oho–6–oho: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
Number of external pieces	50
Level of complexity	5
Related polytopes
Army	Spid
Regiment	Spid
Conjugate	None
Abstract & topological properties
Flag count	720
Euler characteristic	–5
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	No
Nature	Tame

The decahemidecachoron, or duhd, is a nonconvex uniform polychoron that consists of 10 regular tetrahedra and 5 octahemioctahedra. 2 tetrahedra and 3 octahemioctahedra join at each vertex.

Cross-sections

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#444).

• Klitzing, Richard. "duhd".