Demienneract

Demienneract
(OFF file)
Rank	9
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Henne
Coxeter diagram	x3o3o *b3o3o3o3o3o3o ()
Elements
Yotta	256 enneazetta, 18 demiocteracts
Zetta	2304 octaexa, 144 demihepteracts
Exa	9216 heptapeta, 672 demihexeracts
Peta	21504 hexatera, 2016 demipenteracts
Tera	32256 pentachora, 4032 hexadecachora
Cells	5376+32256 tetrahedra
Faces	21504 triangles
Edges	4608
Vertices	256
Vertex figure	Rectified enneazetton, edge length 1
Measures (edge length 1)
Circumradius	$\frac{3\sqrt2}{4} ≈ 1.06066$
Hypervolume	$\frac{2833\sqrt2}{90720} ≈ 0.044163$
Diyottal angles	Hocto–oca–ene: $\arccos\left(-\frac13\right) ≈ 109.47122°$
	Hocto–hesa–hocto: 90°
Height	$\frac{\sqrt2}{2} ≈ 0.70711$
Central density	1
Number of pieces	274
Level of complexity	7
Related polytopes
Army	Henne
Regiment	Henne
Dual	Semistellated pentacosidodecayotton
Conjugate	None
Abstract properties
Euler characteristic	2
Topological properties
Orientable	Yes
Properties
Symmetry	D9, order 92897920
Convex	Yes
Nature	Tame

The demienneract, or henne, also called the hemienneract or 9-demicube, is a convex uniform polyyotton. It has 18 demiocteracts and 256 enneazetta as facets, with 9 of each at a vertex forming a rectified enneazetton as the vertex figure. It is the 9-dimensional demihypercube and is formed by alternating the enneract. It is also a segmentoyotton, as a demiocteractic antiprism.

Vertex coordinates

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

• $\left(\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$

External links

• Klitzing, Richard. "henne".