Hexadecahemidecateron

Hexadecahemidecateron
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Hehad
Coxeter diagram	(x3o3o3o3o3/2*b)/2 (/2)
Elements
Tera	16 pentachora, 5 hexadecachora
Cells	80 tetrahedra
Faces	80 triangles
Edges	40
Vertices	10
Vertex figure	Tesseractihemioctachoron, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Diteral angle	$\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Related polytopes
Army	Tac
Regiment	Tac
Company	Tac
Dual	Hexadecahemidecacron
Conjugate	None
Abstract & topological properties
Flag count	3840
Orientable	No
Properties
Symmetry	D5, order 1920
Flag orbits	2
Convex	No
Nature	Tame

The hexadecahemidecateron, or hehad, is a uniform hemipolyteron. It has 16 regular pentachora and 5 central hexadecachora as facets, with 8 pentachora and 4 hexadecachora at each vertex in the form of a tesseractihemioctachoron. It is the 5D demicross.

It is a faceting of the triacontaditeron, analogous to how the tetrahemihexahedron is a faceting of the octahedron, and the tesseractihemioctachoron is a faceting of the hexadecachoron. It shares the triacontaditeron's vertices, edges, faces, and cells. The 16 pentachora are half of those of the triacontaditeron, while the hexadecachora are its original vertex figures.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 1: Primary Polytera" (#4).

• Klitzing, Richard. "hehad".