Hexamyriapentachiliapentacositriacontahexapedakon

Hexamyriapentachiliapentacositriacontahexapedakon
Rank	16
Type	Regular
Space	Spherical
Notation
Coxeter diagram	o4o3o3o3o3o3o3o3o3o3o3o3o3o3o3x
Schläfli symbol	{3,3,3,3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Pedaka	65536 hexadecatedaka
Tedaka	524288 pentadecatradaka
Tradaka	1966080 tetradecadoka
Doka	4587520 tridecahenda
Henda	7454720 dodecadaka
Daka	8945664 hendecaxenna
Xenna	8200192 decayotta
Yotta	5857280 enneazetta
Zetta	3294720 octaexa
Exa	1464320 heptapeta
Peta	512512 hexatera
Tera	139776 pentachora
Cells	29120 tetrahedra
Faces	4480 triangles
Edges	480
Vertices	32
Vertex figure	Trismyriadischiliaheptacosihexacontoctatedakon, edge length 1
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} \approx 0.70711$
Inradius	$\frac{\sqrt2}{8} \approx 0.17678$
Hypervolume	$\frac{1}{81729648000} \approx 1.2235×10^{-11}$
Dihedral angle	$\arccos\left(-\frac78\right) \approx 151.04498°$
Height	$\frac{\sqrt2}{4} \approx 0.35355$
Central density	1
Number of pieces	65536
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Hexadekeract
Conjugate	None
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B16, order 1371195958099968000
Convex	Yes
Nature	Tame

The hexamyriapentachiliapentacositriacontahexapedakon, also called the hexadecacross or 16-orthoplex, is one of the 3 regular polypedaka. It has 65536 regular hexadecatedaka as facets, joining 4 to a tradakon and 32768 to a vertex in a trismyriadischiliaheptacosihexacontoctatedakal arrangement. It is the 16-dimensional orthoplex. As such it is a diacosipentacontahexazetton duotegum, hexadecachoron tetrategum, and square octategum.

Vertex coordinates

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

• $\left(\pm\frac{\sqrt2}{2},\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0,\,0\right).$