Bitetradecapeton

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:$$\frac{\sqrt{35}}{5}$$ ≈ 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:


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