Tetrachiliaenneacontahexahendon

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Tetrachiliaenneacontahexahendon
Rank12
TypeRegular
SpaceSpherical
Notation
Coxeter diagramo4o3o3o3o3o3o3o3o3o3o3x
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,4}
Elements
Henda4096 dodecadaka
Daka24576 hendecaxenna
Xenna67584 decayotta
Yotta112640 enneazetta
Zetta126720 octaexa
Exa101376 heptapeta
Peta59136 hexatera
Tera25344 pentachora
Cells7920 tetrahedra
Faces1769 triangles
Edges264
Vertices24
Vertex figureDischiliatetracontoctadakon, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of pieces4096
Level of complexity1
Related polytopes
Army*
Regiment*
DualDodekeract
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB12, order 1961990553600
ConvexYes
NatureTame

The tetrachiliaenneacontahexahendon, also called the dodecacross or 12-orthoplex, is one of the 3 regular polyhenda. It has 4096 regular dodecadaka as facets, joining 4 to a xennon and 2048 to a vertex in a dischiliatetracontoctadakal arrangement. It is the 12-dimensional orthoplex. As such, it is a hexacontatetrapeton duotegum, hexadecachoron triotegum, octahedron tetrategum, and square hexategum.

Vertex coordinates[edit | edit source]

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