Octachiliahecatonenneacontadidokon

Octachiliahecatonenneacontadidokon
Rank	13
Type	Regular
Notation
Coxeter diagram	x3o3o3o3o3o3o3o3o3o3o3o4o ()
Schläfli symbol	{3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Doka	8192 tridecahenda
Henda	53248 dodecadaka
Daka	159744 hendecaxenna
Xenna	292864 decayotta
Yotta	366080 enneazetta
Zetta	329472 octaexa
Exa	219648 heptapeta
Peta	109824 hexatera
Tera	41184 pentachora
Cells	11440 tetrahedra
Faces	2288 triangles
Edges	312
Vertices	26
Vertex figure	Tetrachiliaenneacontahexahendon, edge length 1
Measures (edge length 1)
Circumradius	${\frac {\sqrt {2}}{2}}\approx 0.70711$
Inradius	${\frac {\sqrt {26}}{26}}\approx 0.19612$
Hypervolume	${\frac {\sqrt {2}}{97297200}}\approx 1.4535\times 10^{-8}$
Dihedral angle	$\arccos \left(-{\frac {11}{13}}\right)\approx 147.79577^{\circ }$
Height	${\frac {\sqrt {26}}{13}}\approx 0.39223$
Central density	1
Number of external pieces	8192
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Tridekeract
Conjugate	None
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	B13, order 51011754393600
Convex	Yes
Nature	Tame

The octachiliahecatonenneacontadidokon, also called the tridecacross or 13-orthoplex, is a regular polydokon. It has 8192 regular tridecahenda as facets, joining 4 to a peak and 4096 to a vertex in a tetrachiliaenneacontahexahendal arrangement. It is the 13-dimensional orthoplex.

Vertex coordinates

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

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