Pentacosidodecayotton

Pentacosidodecayotton
(OFF file)
Rank	9
Type	Regular
Notation
Bowers style acronym	Vee
Coxeter diagram	o4o3o3o3o3o3o3o3x ()
Schläfli symbol	{3,3,3,3,3,3,3,4}
Bracket notation	<IIIIIIIII>
Elements
Yotta	512 enneazetta
Zetta	2304 octaexa
Exa	4608 heptapeta
Peta	5376 hexatera
Tera	4032 pentachora
Cells	2016 tetrahedra
Faces	672 triangles
Edges	144
Vertices	18
Vertex figure	Diacosipentacontahexazetton, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Inradius	${\frac {\sqrt {2}}{6}}\approx 0.23570$
Hypervolume	${\frac {\sqrt {2}}{22680}}\approx 0.000062355$
Diyottal angle	$\arccos \left(-{\frac {7}{9}}\right)\approx 141.05756^{\circ }$
Height	${\frac {\sqrt {2}}{3}}\approx 0.47140$
Central density	1
Number of external pieces	512
Level of complexity	1
Related polytopes
Army	Vee
Regiment	Vee
Dual	Enneract
Conjugate	None
Abstract & topological properties
Flag count	185794560
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B9, order 185794560
Convex	Yes
Net count	248639631948
Nature	Tame

The pentacosidodecayotton, or vee, also called the enneacross or 9-orthoplex, is one of the 3 regular polyyotta. It has 512 regular enneazetta as facets, joining 4 to a heptapeton peak and 256 to a vertex in a diacosipentacontahexazettal arrangement. It is the 9-dimensional orthoplex. It is also an octahedron triotegum.

Vertex coordinates

The vertices of a regular pentacosidodecayotton of edge length 1, centered at the origin, are given by all permutations of:

• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right)$.

External links

• Klitzing, Richard. "vee".

• Wikipedia Contributors. "9-orthoplex".