Myriahexachiliatriacosioctacontatetratradakon

Myriahexachiliatriacosioctacontatetratradakon
Rank	14
Type	Regular
Space	Spherical
Notation
Coxeter diagram	o4o3o3o3o3o3o3o3o3o3o3o3o3x
Schläfli symbol	{3,3,3,3,3,3,3,3,3,3,3,3,4}
Elements
Tradaka	16384 tetradecadoka
Doka	114688 tridecahenda
Henda	372736 dodecadaka
Daka	745472 hendecaxenna
Xenna	1025024 decayotta
Yotta	1025024 enneazetta
Zetta	768768 octaexa
Exa	439296 heptapeta
Peta	192192 hexatera
Tera	64064 pentachora
Cells	16016 tetrahedra
Faces	2912 triangles
Edges	364
Vertices	28
Vertex figure	Octachiliahecatonenneacontadidokon, edge length 1
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} \approx 0.70711$
Inradius	$\frac{\sqrt7}{14} \approx 0.18898$
Hypervolume	$\frac{1}{681080400} \approx 1.4683×10^{-9}$
Dihedral angle	$\arccos\left(-\frac67\right) \approx 148.99728°$
Height	$\frac{\sqrt7}{7} \approx 0.37796$
Central density	1
Number of pieces	16384
Level of complexity	1
Related polytopes
Army	*
Regiment	*
Dual	Tetradekeract
Conjugate	None
Abstract properties
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	B14, order 1428329123020800
Convex	Yes
Nature	Tame

The myriahexachiliatriacosioctacontatetratradakon, also called the tetradecacross or 14-orthoplex, is one of the 3 regular polytradaka. It has 16384 regular tetradecadoka as facets, joining 4 to a hendon and 8192 to a vertex in a octachiliahecatonenneacontadidokal arrangement. It is the 14-dimensional orthoplex. As such, it is a hecatonicosoctaexon duotegum and square heptategum.

Vertex coordinates

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

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