9-demicube

9-demicube
Rank	9
Type	Uniform
Notation
Bowers style acronym	Henne
Coxeter diagram	x3o3o3o3o3o3o3o *b3o ()
Elements
Yotta	256 8-simplices 18 8-demicubes
Zetta	2304 7-simplices 144 7-demicubes
Exa	9216 6-simplices 672 6-demicubes
Peta	21504 5-simplices 2016 5-demicubes
Tera	32256 pentachora 4032 hexadecachora
Cells	5376+32256 tetrahedra
Faces	21504 triangles
Edges	4608
Vertices	256
Vertex figure	Rectified 8-simplex, edge length 1
Measures (edge length 1)
Circumradius	${\frac {3{\sqrt {2}}}{4}}\approx 1.06066$
Hypervolume	${\frac {2833{\sqrt {2}}}{90720}}\approx 0.044163$
Diyottal angles	Hocto–oca–ene: $\arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }$
	Hocto–hesa–hocto: 90°
Height	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Number of external pieces	274
Level of complexity	7
Related polytopes
Army	Henne
Regiment	Henne
Dual	Semistellated pentacosidodecayotton
Conjugate	None
Abstract & topological properties
Flag count	650280960
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	D9, order 92897920
Flag orbits	7
Convex	Yes
Nature	Tame

The 9-demicube, also called the hemienneract, demienneract, or henne, is a convex uniform 9-polytope. It has 18 8-demicubes and 256 8-simplices as facets, with 9 of each at a vertex forming a rectified 8-simplex as the vertex figure. It is the 9-dimensional demihypercube and is formed by alternating the 9-cube. It is also a segmentoyotton, as a 8-demicubic antiprism.

Vertex coordinates

The vertices of a 9-demicube of edge length 1, centered at the origin, are given by all even sign changes of:

• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}}\right)$.

External links

• Klitzing, Richard. "henne".