quil

Acronym	quil
Name	pentacosiheptacontihexa-pentacontihexa-exon, vertex figure of yab
Circumradius	sqrt(3)/2 = 0.866025
Coordinates	(sqrt(2); 2, 0, 0, 0, 0, 0)/sqrt(8) & all permutations in all but first coord, all changes of sign (2 × 12 vertices: top and bottom gee) (0; 1, 1, 1, 1, 1, 1)/sqrt(8) & all permutations and all even changes of sign in all but first coord (32 vertices: equatorial hax)
Colonel of regiment	naq
Face vector	56, 756, 4032, 10080, 12096, 4788, 632

Incidence matrix

  56 ♦  27 |  216 |   720 |  1080 |  432 135 |  72 27
-----+-----+------+-------+-------+----------+-------
   2 | 756 ♦   16 |    80 |   160 |   80  40 |  16 16
-----+-----+------+-------+-------+----------+-------
   3 |   3 | 4032 ♦    10 |    30 |   20  15 |   5 10
-----+-----+------+-------+-------+----------+-------
♦  4 |   6 |    4 | 10080 |     6 |    6   6 |   2  6
-----+-----+------+-------+-------+----------+-------
♦  5 |  10 |   10 |     5 | 12096 |    2   2 |   1  3
-----+-----+------+-------+-------+----------+-------
♦  6 |  15 |   20 |    15 |     6 | 4032   * |   1  1
♦ 10 |  40 |   80 |    80 |    32 |    * 756 |   0  2
-----+-----+------+-------+-------+----------+-------
♦  7 |  21 |   35 |    35 |    21 |    7   0 | 576  *
♦ 27 | 216 |  720 |  1080 |   648 |   72  27 |   * 56

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