# Bitruncated hexateron

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Bitruncated hexateron
Rank5
TypeUniform
SpaceSpherical
Notation
Bowers style acronymBittix
Coxeter diagramo3x3x3o3o ()
Elements
Tera6 truncated pentachora, 6 decachora
Cells15 tetrahedra, 15+30 truncated tetrahedra
Faces20+60 triangles, 60 hexagons
Edges60+90
Vertices60
Vertex figureTriangular scalene, edge lengths 1 (base triangle and top edge) and 3 (sides)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{87}}{6} ≈ 1.55456}$
Hypervolume${\displaystyle \frac{841\sqrt3}{240} ≈ 6.06939}$
Diteral anglesDeca–tut–tip: ${\displaystyle \arccos\left(-\frac15\right) ≈ 101.53696^\circ}$
Tip–tet–tip: ${\displaystyle \arccos\left(\frac15\right) ≈ 78.46304^\circ}$
Deca–tut–deca: ${\displaystyle \arccos\left(\frac15\right) ≈ 78.46304^\circ}$
Central density1
Number of external pieces12
Level of complexity10
Related polytopes
ArmyBittix
RegimentBittix
DualTriangular-scalenic hexecontateron
ConjugateNone
Abstract & topological properties
Flag count7200
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
ConvexYes
NatureTame

The bitruncated hexateron, or bittix, also called the bitruncated 5-simplex, is a convex uniform polyteron. It consists of 6 truncated pentachora and 6 decachora. 2 truncated pentachora and 3 decachora join at each vertex. As the name suggests, it is the bitruncation of the hexateron.

## Vertex coordinates

The vertices of a bitruncated hexateron of edge length 1 can be given in 6 dimensions as all permutations of:

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

## Representations

A bitruncated hexateron has the following Coxeter diagrams:

• o3x3x3o3o (full symmetry)
• oox3xux3xoo3ooo&#xt (A4 axial, decachoron-first)

## Related polytopes

o3o3o3o3o truncations
Name OBSA CD diagram Picture
Hexateron hix
Rectified hexateron rix
Dodecateron dot
Rectified hexateron rix
Hexateron hix
Truncated hexateron tix
Bitruncated hexateron bittix
Bitruncated hexateron bittix
Truncated hexateron tix
Small rhombated hexateron sarx
Small birhombidodecateron sibrid
Small rhombated hexateron sarx
Great rhombated hexateron garx
Great birhombidodecateron gibrid
Great rhombated hexateron garx
Small prismated hexateron spix
Small prismated hexateron spix
Prismatotruncated hexateron pattix
Prismatorhombated hexateron pirx
Prismatorhombated hexateron pirx
Prismatotruncated hexateron pattix
Great prismated hexateron gippix
Great prismated hexateron gippix
Small cellidodecateron scad
Celliprismated hexateron cappix
Cellirhombidodecateron card
Celligreatorhombated hexateron cograx
Celliprismated hexateron cappix
Celliprismatotruncatododecateron captid
Celligreatorhombated hexateron cograx
Great cellidodecateron gocad