Bitetradecapeton

Bitetradecapeton
File:Bitetradecapeton.png (OFF file)
Rank	6
Type	Noble
Notation
Bowers style acronym	Bife
Elements
Peta	140 triangular disphenoids
Tera	420 triangular scalenes
Cells	210 tetragonal disphenoids, 280 triangular pyramids
Faces	70 triangles, 210 isosceles triangles
Edges	42+42
Vertices	14
Vertex figure	Triangular-scalenic hexecontateron
Measures (edge length 1)
Central density	1
Related polytopes
Dual	Tetradecapeton
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A6×2, order 10080
Convex	Yes
Nature	Tame

The bitetradecapeton or bife, also known as the triangular-disphenoidal hecatontetracontapeton, is a convex noble polypeton with 140 identical triangular disphenoids as peta. 60 facets join at each vertex. It can be obained as the dual of the uniform tetradecapeton.

It is also the convex hull of a heptapeton and its central inversion, as well as the 14-3-5 step prism.

The ratio between the longest and shortest edges is $1:{\frac {\sqrt {35}}{5}}\approx 1:1.18322$.

Vertex coordinates

The vertices of a bitetradecapeton, based on two heptapeta of edge length 1, centered at the origin, are given by:

• $\pm \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,-{\frac {\sqrt {6}}{12}},\,-{\frac {\sqrt {10}}{20}},\,-{\frac {\sqrt {15}}{30}},\,-{\frac {\sqrt {21}}{42}}\right),$
• $\pm \left(0,\,{\frac {\sqrt {3}}{3}},\,-{\frac {\sqrt {6}}{12}},\,-{\frac {\sqrt {10}}{20}},\,-{\frac {\sqrt {15}}{30}},\,-{\frac {\sqrt {21}}{42}}\right),$
• $\pm \left(0,\,0,\,{\frac {\sqrt {6}}{4}},\,-{\frac {\sqrt {10}}{20}},\,-{\frac {\sqrt {15}}{30}},\,-{\frac {\sqrt {21}}{42}}\right),$
• $\pm \left(0,\,0,\,0,\,{\frac {\sqrt {10}}{5}},\,-{\frac {\sqrt {15}}{30}},\,-{\frac {\sqrt {21}}{42}}\right),$
• $\pm \left(0,\,0,\,0,\,0,\,{\frac {\sqrt {15}}{6}},\,-{\frac {\sqrt {21}}{42}}\right),$
• $\left(0,\,0,\,0,\,0,\,0,\,\pm {\frac {\sqrt {21}}{7}}\right).$