Acronym haxip
Name hemihexeractic prism,
vertex figure of rinquoh
Circumradius 3/sqrt(8) = 1.060660
Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/2)   & all even changes of sign in all but last coord., change of sign in last coord.
Confer
general polytopal classes:
segmentoexa  

Incidence matrix according to Dynkin symbol

x x3o3o *c3o3o3o

o o3o3o *c3o3o3o | 64 |  1  15 |  15   60 |  60  20  60 |  20  60  15  30 | 15  30  6  6 |  6  6 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x . . .    . . . |  2 | 32   *   15    0 |  60   0   0 |  20  60   0   0 | 15  30  0  0 |  6  6 0
. x . .    . . . |  2 |  * 480 |   1    8 |   8   4  12 |   4  12   6   8 |  6   8  4  2 |  4  2 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x x . .    . . . |  4 |  2   2 | 240    *    8   0   0 |   4  12   0   0 |  6   8  0  0 |  4  2 0
. x3o .    . . . |  3 |  0   3 |   * 1280 |   1   1   3 |   1   3   3   3 |  3   3  3  1 |  3  1 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x x3o .    . . .   6 |  3   6 |   3    2 | 640   *   * |   1   3   0   0 |  3   3  0  0 |  3  1 0
. x3o3o    . . .   4 |  0   6 |   0    4 |   * 320   * |   1   0   3   0 |  3   0  3  0 |  3  0 1
. x3o . *c3o . .   4 |  0   6 |   0    4 |   *   * 960 |   0   1   1   2 |  1   2  2  1 |  2  1 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x x3o3o    . . .   8 |  4  12 |   6    8 |   4   2   0 | 160   *   *   * |  3   0  0  0 |  3  0 0
x x3o . *c3o . .   8 |  4  12 |   6    8 |   4   0   2 |   * 480   *   * |  1   2  0  0 |  2  1 0
. x3o3o *c3o . .   8 |  0  24 |   0   32 |   0   8   8 |   *   * 120   * |  1   0  2  0 |  2  0 1
. x3o . *c3o3o .   5 |  0  10 |   0   10 |   0   0   5 |   *   *   * 384 |  0   1  1  1 |  1  1 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x x3o3o *c3o . .  16 |  8  48 |  24   64 |  32  16  16 |   8   8   2   0 | 60   *  *  * |  2  0 0
x x3o . *c3o3o .  10 |  5  20 |  10   20 |  10   0  10 |   0   5   0   2 |  * 192  *  * |  1  1 0
. x3o3o *c3o3o .  16 |  0  80 |   0  160 |   0  40  80 |   0   0  10  16 |  *   * 24  * |  1  0 1
. x3o . *c3o3o3o   6 |  0  15 |   0   20 |   0   0  15 |   0   0   0   6 |  *   *  * 64 |  0  1 1
-----------------+----+--------+----------+-------------+-----------------+--------------+--------
x x3o3o *c3o3o .  32 | 16 160 |  80  320 | 160  80 160 |  40  80  20  32 | 10  16  2  0 | 12  * *
x x3o . *c3o3o3o  12 |  6  30 |  15   40 |  20   0  30 |   0  15   0  12 |  0   6  0  2 |  * 32 *
. x3o3o *c3o3o3o  32 |  0 240 |   0  640 |   0 160 480 |   0   0  60 192 |  0   0 12 32 |  *  * 2

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