Acronym	kaje
Name	heptacontidiaicosiheptapeton, vertex figure of quil
Circumradius	sqrt(2/3) = 0.816497
Coordinates	(0, 0, 0, 0, 0; sqrt(2/3)) (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 1/sqrt(24))    & all even changes of sign in one but last coord. (1/sqrt(2), 0, 0, 0, 0; -1/sqrt(6))                                                  & all permutations and all changes of sign in one but last coord.
Colonel of regiment	jak
Face vector	27, 216, 720, 1080, 567, 99
Confer	2kaje
External links

Incidence matrix

  27 ♦  16 |  80 |  160 |  80  40 | 16 16
-----+-----+-----+------+---------+------
   2 | 216 ♦  10 |   30 |  20  15 |  5 10
-----+-----+-----+------+---------+------
   3 |   3 | 720 |    6 |   6   6 |  2  6
-----+-----+-----+------+---------+------
♦  4 |   6 |   4 | 1080 |   2   2 |  1  3
-----+-----+-----+------+---------+------
♦  5 |  10 |  10 |    5 | 432   * |  1  1
♦  8 |  24 |  32 |   16 |   * 135 |  0  2
-----+-----+-----+------+---------+------
♦  6 |  15 |  20 |   15 |   6   0 | 72  *
♦ 16 |  80 | 160 |  120 |  16  10 |  * 27