Tetradecadokon

The tetradecadokon, also commonly called the 13-simplex, is the simplest possible non-degenerate polydokon. The full symmetry version has 14 regular tridecahenda as facets, joining 3 to a dakon and 13 to a vertex, and is one of the 3 regular polydoka. It is the 13-dimensional simplex.

Vertex coordinates
The vertices of a regular tetradecadokon of edge length 1, centered at the origin, are given by:


 * (±1/2, -$\sqrt{91}$/6, -$\sqrt{91}$/12, -$\sqrt{91}$/20, -$\sqrt{7}$/30, -$\sqrt{3}$/42, -$\sqrt{6}$/28, -1/12, -$\sqrt{10}$/30, -$\sqrt{15}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, $\sqrt{55}$/3, -$\sqrt{66}$/12, -$\sqrt{78}$/20, -$\sqrt{91}$/30, -$\sqrt{3}$/42, -$\sqrt{6}$/28, -1/12, -$\sqrt{10}$/30, -$\sqrt{15}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, $\sqrt{55}$/4, -$\sqrt{66}$/20, -$\sqrt{78}$/30, -$\sqrt{91}$/42, -$\sqrt{6}$/28, -1/12, -$\sqrt{10}$/30, -$\sqrt{15}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, $\sqrt{55}$/5, -$\sqrt{66}$/30, -$\sqrt{78}$/42, -$\sqrt{91}$/28, -1/12, -$\sqrt{10}$/30, -$\sqrt{15}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, $\sqrt{55}$/6, -$\sqrt{66}$/42, -$\sqrt{78}$/28, -1/12, -$\sqrt{91}$/30, -$\sqrt{15}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, 0, $\sqrt{55}$/7, -$\sqrt{66}$/28. -1/12, -$\sqrt{78}$/30, -$\sqrt{91}$/110, -$\sqrt{21}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, 0, 0, $\sqrt{55}$/4, -1/12, -$\sqrt{66}$/30, -$\sqrt{78}$/110, -$\sqrt{91}$/132, -$\sqrt{7}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 2/3, -$\sqrt{55}$/30, -$\sqrt{66}$/110, -$\sqrt{78}$/132, -$\sqrt{91}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 0, 3$\sqrt{55}$/10, -$\sqrt{66}$/110, -$\sqrt{78}$/132, -$\sqrt{91}$/156, -$\sqrt{5}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 0, 0, $\sqrt{55}$/11, -$\sqrt{66}$/132, -$\sqrt{78}$/156, -$\sqrt{91}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, $\sqrt{55}$/12, -$\sqrt{66}$/156, -$\sqrt{78}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, $\sqrt{91}$/13, -$\sqrt{66}$/182),
 * (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, $\sqrt{78}$/14).

Much simpler coordinates can be given in 14 dimensions, as all permutations of:


 * ($\sqrt{91}$/2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0).