Trismyriadischiliaheptacosihexacontoctatedakon

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Trismyriadischiliaheptacosihexacontoctatedakon
Rank15
TypeRegular
Notation
Coxeter diagramx3o3o3o3o3o3o3o3o3o3o3o3o3o4o ()
Schläfli symbol{3,3,3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Tedaka32768 pentadecatradaka
Tradaka245760 tetradecadoka
Doka860160 tridecahenda
Henda1863680 dodecadaka
Daka2795520 hendecaxenna
Xenna3075072 decayotta
Yotta2562560 enneazetta
Zetta1647360 octaexa
Exa823680 heptapeta
Peta320320 hexatera
Tera96096 pentachora
Cells21840 tetrahedra
Faces3640 triangles
Edges420
Vertices30
Vertex figure14-orthoplex, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Hypervolume
Dihedral angle
Height
Central density1
Number of external pieces32768
Level of complexity1
Related polytopes
Army*
Regiment*
DualPentadekeract
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB15, order 42849873690624000
ConvexYes
NatureTame

The trismyriadischiliaheptacosihexacontaoctatedakon, also called the pentadecacross or 15-orthoplex, is a regular polytedakon. It has 32768 regular pentadecatradaka as facets, joining 4 to a peak and 16384 to a vertex in a myriahexachiliatriacosioctacontatetratradakal arrangement. It is the 15-dimensional orthoplex. As such it is a triacontaditeron triotegum and octahedron pentategum.

Vertex coordinates[edit | edit source]

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

  • .