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
Pedaka65536 hexadecatedaka
Tedaka524288 pentadecatradaka
Tradaka1966080 tetradecadoka
Doka4587520 tridecahenda
Henda7454720 dodecadaka
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
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces65536
Level of complexity1
Related polytopes
Army*
Regiment*
DualHexadekeract
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB16, order 1371195958099968000
ConvexYes
NatureTame

Vertex coordinates edit

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

  •  .