Demidekeract

Demidekeract
(OFF file)
Rank	10
Type	Uniform
Notation
Bowers style acronym	Hede
Coxeter diagram	x3o3o3o3o3o3o3o3o *b3o ()
Elements
Xenna	512 decayotta, 20 demienneracts
Yotta	5120 enneazetta, 180 demiocteracts
Zetta	23040 octaexa, 960 demihepteracts
Exa	61440 heptapeta, 3360 demihexeracts
Peta	107520 hexatera, 8064 demipenteracts
Tera	129024 pentachora, 7680 hexadecachora
Cells	15360+107520 tetrahedra
Faces	61440 triangles
Edges	11520
Vertices	512
Vertex figure	Rectified decayotton, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {5}}{2}}\approx 1.11803$
Hypervolume	${\frac {14137}{453600}}\approx 0.031246$
Dixennal angles	Henne–ene–day: $\arccos \left(-{\frac {\sqrt {10}}{10}}\right)\approx 108.43495^{\circ }$
	Henne–hocto–henne: 90°
Height	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Central density	1
Number of external pieces	532
Level of complexity	8
Related polytopes
Army	Hede
Regiment	Hede
Dual	Semistellated chiliaicositetraxennon
Conjugate	None
Abstract & topological properties
Flag count	14863564800
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	D10, order 1857945600
Convex	Yes
Nature	Tame

The demidekeract, or hede, also called the hemidekeract or 10-demicube, is a convex uniform polyxennon. It has 20 demienneracts and 512 decayotta as facets, with 10 of each at a vertex forming a rectified decayotton as the vertex figure. It is the 10-dimensional demihypercube and is formed by alternating the dekeract. It is also a segmentoxennon, as a demienneractic alterprism.

Vertex coordinates

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

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

External links

• Klitzing, Richard. "hede".