# Hexamyriapentachiliapentacositriacontahexapedakon

The hexamyriapentachiliapentacositriacontahexapedakon, also called the hexadecacross or 16-orthoplex, is a regular polypedakon. 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.

Hexamyriapentachiliapentacositriacontahexapedakon
Rank16
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o3o3o4o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Doka4587520 tridecahenda
Daka8945664 hendecaxenna
Xenna8200192 decayotta
Yotta5857280 enneazetta
Zetta3294720 octaexa
Exa1464320 heptapeta
Peta512512 hexatera
Tera139776 pentachora
Cells29120 tetrahedra
Faces4480 triangles
Edges480
Vertices32
Vertex figure15-orthoplex, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2}}\approx 0.70711}$
Inradius${\displaystyle {\frac {\sqrt {2}}{8}}\approx 0.17678}$
Hypervolume${\displaystyle {\frac {1}{81729648000}}\approx 1.2235\times 10^{-11}}$
Dihedral angle${\displaystyle \arccos \left(-{\frac {7}{8}}\right)\approx 151.04498^{\circ }}$
Height${\displaystyle {\frac {\sqrt {2}}{4}}\approx 0.35355}$
Central density1
Number of external pieces65536
Level of complexity1
Related polytopes
Army*
Regiment*
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB16, order 1371195958099968000
ConvexYes
NatureTame

## Vertex coordinates

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

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