Bidodecateric heptacontadipeton

Bidodecateric heptacontadipeton
File:Bidodecateric heptacontadipeton.png (OFF file)
Rank	6
Type	Noble
Notation
Coxeter diagram	o3o3o3o3o *c3m
Elements
Peta	72 bidodecatera
Tera	720 triangular duotegums
Cells	2160 tetragonal disphenoids
Faces	2160 isosceles triangles
Edges	270+432
Vertices	54
Vertex figure	Semistellated triacontaditeron
Measures (based on two icosiheptaheptaontadipeta of edge length 1)
Edge lengths	Lacing edges (270): ${\frac {\sqrt {6}}{3}}\approx 0.81650$
	Base edges (432): 1
Circumradius	${\frac {\sqrt {6}}{3}}\approx 0.81650$
Inradius	${\frac {1}{2}}=0.5$
Dipetal angle	120°
Central density	1
Related polytopes
Dual	122 polytope
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	E6×2, order 103680
Convex	Yes
Nature	Tame

The bidodecateric heptacontadipeton, is a convex noble 6-polytope with 72 identical bidodecatera as facets. It can be obtained as the convex hull of the 2₂₁ polytope and its central inversion, with pairs of hexateral facets lying in common hyperplanes.

The ratio between the longest and shortest edges is $1:{\frac {\sqrt {6}}{2}}\approx 1:1.22474$.

Vertex coordinates

Coordinates for the vertices of a bidodecateric heptacontadipeton, based on two icosiheptaheptacontadipeta of edge length 1, centered at the origin, are given by:

• $\left(0,\,0,\,0,\,0,\,0,\,\pm {\frac {\sqrt {6}}{3}}\right)$,
• $\left({\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {2}}{4}},\,{\frac {\sqrt {6}}{12}}\right)$ and all even sign changes,
• $\left(\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,0,\,0,\,\pm {\frac {\sqrt {6}}{6}}\right)$ and all permutations of first 5 coordinates.

External links

• Klitzing, Richard. "o3o3o3o3o *c3m".