Dishexadecateron

Dishexadecateron
File:Dishexadecateron.png (OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Dah
Coxeter diagram	(x3o3o3o3o3/2*1)/2 (/2)
Elements
Tera	16 pentachora, 16 rectified pentachora
Cells	80 tetrahedra, 40 octahedra
Faces	160 triangles
Edges	80
Vertices	16
Vertex figure	Faceted rectified pentachoron, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {10}}{4}}\approx 0.79057$
Hypervolume	${\frac {\sqrt {2}}{15}}\approx 0.094281$
Diteral angles	Pen–tet–rap: $\arccos \left({\frac {3}{5}}\right)\approx 53.13010^{\circ }$
	Rap–oct–rap: $\arccos \left({\frac {3}{5}}\right)\approx 53.13010^{\circ }$
Related polytopes
Army	Hin
Regiment	Hin
Conjugate	None
Abstract & topological properties
Flag count	7680
Orientable	Yes
Properties
Symmetry	D5, order 1920
Convex	No
Nature	Tame

The dishexadecateron or dah is a nonconvex uniform polyteron that consists of 16 pentachora and 16 rectified pentachora. 5 pentachora and 10 rectified pentachora form its faceted rectified pentachoric vertex figure; its facial structure is identical to that of the demipenteract, as their vertex figures fall into the same regiment.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 1: Primary Polytera" (#8).

• Klitzing, Richard. "dah".