Decayotton

The decayotton, or day, also commonly called the 9-simplex, is the simplest possible non-degenerate polyyotton. The full symmetry version has 9 regular enneazetta as facets, joining 3 to a heptapeton peak and 9 to a vertex, and is one of the 3 regular polyzetta. It is the 9-dimensional simplex.

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


 * (±1/2, –$\sqrt{5}$/6, –$\sqrt{5}$/12, –$\sqrt{5}$/20, –$\sqrt{5}$/30, –$\sqrt{3}$/42, –$\sqrt{6}$/28, –1/12, –$\sqrt{10}$/30),
 * (0, $\sqrt{15}$/3, –$\sqrt{21}$/12, –$\sqrt{7}$/20, –$\sqrt{5}$/30, –$\sqrt{3}$/42, –$\sqrt{6}$/28, –1/12, –$\sqrt{10}$/30),
 * (0, 0, $\sqrt{15}$/4, –$\sqrt{21}$/20, –$\sqrt{7}$/30, –$\sqrt{5}$/42, –$\sqrt{6}$/28, –1/12, –$\sqrt{10}$/30),
 * (0, 0, 0, $\sqrt{15}$/5, –$\sqrt{21}$/30, –$\sqrt{7}$/42, –$\sqrt{5}$/28, –1/12, –$\sqrt{10}$/30),
 * (0, 0, 0, 0, $\sqrt{15}$/6, –$\sqrt{21}$/42, –$\sqrt{7}$/28, –1/12, –$\sqrt{5}$/30),
 * (0, 0, 0, 0, 0, $\sqrt{15}$/7, –$\sqrt{21}$/28. –1/12, –$\sqrt{7}$/30),
 * (0, 0, 0, 0, 0, 0, $\sqrt{5}$/4, –1/12, –$\sqrt{21}$/30),
 * (0, 0, 0, 0, 0, 0, 0, 2/3, –$\sqrt{7}$/30),
 * (0, 0, 0, 0, 0, 0, 0, 0, 3$\sqrt{5}$/10).

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


 * ($\sqrt{7}$/2, 0, 0, 0, 0, 0, 0, 0, 0, 0).