Acronym gahax
Name gee atop hax,
gee-first segment of naq
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art 
o    		where:
    H		H = x3o3o *b3o3o (hin)
T    		h = o3o3x *b3o3o (alternate hin)
    h		T = o3o3o *b3o3x (tac)
o    		o = o3o3o *b3o3o (point)
     
|   +	x3o3o *b3o3o3o (hax)
+----	o3o3o *b3o3o3x (gee)
Coordinates
  1. (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 0)    & all even changes of sign in one but last coord.
    (right hax layer)
  2. (1/sqrt(2), 0, 0, 0, 0, 0, -1/sqrt(2))                               & all permutations, all changes of sign in one but last coord.
    (left gee layer)
Face vector 44, 492, 2240, 4880, 5244, 2452, 298
Confer
uniform relative:
naq  
related CRFs:
Dutour's polyexon type A  
general polytopal classes:
segmentoexa   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

xo3oo3oo *b3oo3oo3ox&#x   → height = 1/2
(gee || hax)

o.3o.3o. *b3o.3o.3o.    | 32  * |  15   6  0 |  60  60  15   0 |  20  60  180   90  20   0 | 15  30  60 120  180  60  15   0 |  6  6  30  30  60  60  60  15   6  0  0 | 1  6 15  20  6  1 0
.o3.o3.o *b3.o3.o3.o    |  * 12 ♦   0  16 10 |   0  80  80  40 |   0   0  160  240 160  80 |  0   0  40  80  320 240 160  80 |  0  0  10  16  80  80 160  60  80 16 16 | 0  1 10  40 16 16 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x. .. ..    .. .. ..    |  2  0 | 240   *  * |   8   4   0   0 |   4  12   24    6   0   0 |  6   8  12  24   24   4   0   0 |  4  2  12   8  12  12   8   1   0  0  0 | 1  4  6   4  2  0 0
oo3oo3oo *b3oo3oo3oo&#x |  1  1 |   * 192  * |   0  10   5   0 |   0   0   30   30  10   0 |  0   0  10  20   60  30  10   0 |  0  0   5   5  20  20  30  10   5  0  0 | 0  1  5  10  5  1 0
.. .. ..    .. .. .x    |  0  2 |   *   * 60 ♦   0   0   8   8 |   0   0    0   24  32  24 |  0   0   0   0   32  48  48  32 |  0  0   0   0   8   8  32  24  32  8  8 | 0  0  1   8  8  8 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x.3o. ..    .. .. ..    |  3  0 |   3   0  0 | 640   *   *   * |   1   3    3    0   0   0 |  3   3   3   6    3   0   0   0 |  3  1   6   3   3   3   1   0   0  0  0 | 1  3  3   1  1  0 0
xo .. ..    .. .. ..&#x |  2  1 |   1   2  0 |   * 960   *   * |   0   0    6    3   0   0 |  0   0   3   6   12   3   0   0 |  0  0   3   2   6   6   6   1   0  0  0 | 0  1  3   3  2  0 0
.. .. ..    .. .. ox&#x |  1  2 |   0   2  1 |   *   * 480   * |   0   0    0    6   4   0 |  0   0   0   0   12  12   6   0 |  0  0   0   0   4   4  12   6   4  0  0 | 0  0  1   4  4  1 0
.. .. ..    .. .o3.x    |  0  3 |   0   0  3 |   *   *   * 160 ♦   0   0    0    0   4   6 |  0   0   0   0    0   6  12  12 |  0  0   0   0   0   0   4   6  12  4  4 | 0  0  0   1  4  4 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x.3o.3o.    .. .. ..    ♦  4  0 |   6   0  0 |   4   0   0   0 | 160   *    *    *   *   * |  3   0   3   0    0   0   0   0 |  3  0   6   0   3   0   0   0   0  0  0 | 1  3  3   1  0  0 0
x.3o. .. *b3o. .. ..    ♦  4  0 |   6   0  0 |   4   0   0   0 |   * 480    *    *   *   * |  1   2   0   2    0   0   0   0 |  2  1   2   2   0   1   0   0   0  0  0 | 1  2  1   0  1  0 0
xo3oo ..    .. .. ..&#x ♦  3  1 |   3   3  0 |   1   3   0   0 |   *   * 1920    *   *   * |  0   0   1   2    2   0   0   0 |  0  0   2   1   2   2   1   0   0  0  0 | 0  1  2   1  1  0 0
xo .. ..    .. .. ox&#x ♦  2  2 |   1   4  1 |   0   2   2   0 |   *   *    * 1440   *   * |  0   0   0   0    4   2   0   0 |  0  0   0   0   2   2   4   1   0  0  0 | 0  0  1   2  2  0 0
.. .. ..    .. oo3ox&#x ♦  1  3 |   0   3  3 |   0   0   3   1 |   *   *    *    * 640   * ♦  0   0   0   0    0   3   3   0 |  0  0   0   0   0   0   3   3   3  0  0 | 0  0  0   1  3  1 0
.. .. ..    .o3.o3.x    ♦  0  4 |   0   0  6 |   0   0   0   4 |   *   *    *    *   * 240 ♦  0   0   0   0    0   0   2   4 |  0  0   0   0   0   0   0   1   4  2  2 | 0  0  0   0  2  2 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x.3o.3o. *b3o. .. ..    ♦  8  0 |  24   0  0 |  32   0   0   0 |   8   8    0    0   0   0 | 60   *   *   *    *   *   *   * |  2  0   2   0   0   0   0   0   0  0  0 | 1  2  1   0  0  0 0
x.3o. .. *b3o.3o. ..    ♦  5  0 |  10   0  0 |  10   0   0   0 |   0   5    0    0   0   0 |  * 192   *   *    *   *   *   * |  1  1   0   1   0   0   0   0   0  0  0 | 1  1  0   0  1  0 0
xo3oo3oo    .. .. ..&#x ♦  4  1 |   6   4  0 |   4   6   0   0 |   1   0    4    0   0   0 |  *   * 480   *    *   *   *   * |  0  0   2   0   2   0   0   0   0  0  0 | 0  1  2   1  0  0 0
xo3oo .. *b3oo .. ..&#x ♦  4  1 |   6   4  0 |   4   6   0   0 |   0   1    4    0   0   0 |  *   *   * 960    *   *   *   * |  0  0   1   1   0   1   0   0   0  0  0 | 0  1  1   0  1  0 0
xo3oo ..    .. .. ox&#x ♦  3  2 |   3   6  1 |   1   6   3   0 |   0   0    2    3   0   0 |  *   *   *   * 1920   *   *   * |  0  0   0   0   1   1   1   0   0  0  0 | 0  0  1   1  1  0 0
xo .. ..    .. oo3ox&#x ♦  2  3 |   1   6  3 |   0   3   6   1 |   0   0    0    3   2   0 |  *   *   *   *    * 960   *   * |  0  0   0   0   0   0   2   1   0  0  0 | 0  0  0   1  2  0 0
.. .. ..    oo3oo3ox&#x ♦  1  4 |   0   4  6 |   0   0   6   4 |   0   0    0    0   4   1 |  *   *   *   *    *   * 480   * |  0  0   0   0   0   0   0   1   2  0  0 | 0  0  0   0  2  1 0
.. .o .. *b3.o3.o3.x    ♦  0  5 |   0   0 10 |   0   0   0  10 |   0   0    0    0   0   5 |  *   *   *   *    *   *   * 192 |  0  0   0   0   0   0   0   0   1  1  1 | 0  0  0   0  1  1 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x.3o.3o. *b3o.3o. ..&#x ♦ 16  0 |  80   0  0 | 160   0   0   0 |  40  80    0    0   0   0 | 10  16   0   0    0   0   0   0 | 12  *   *   *   *   *   *   *   *  *  * | 1  1  0   0  0  0 0
x.3o. .. *b3o.3o.3o.    ♦  6  0 |  15   0  0 |  20   0   0   0 |   0  15    0    0   0   0 |  0   6   0   0    0   0   0   0 |  * 32   *   *   *   *   *   *   *  *  * | 1  0  0   0  1  0 0
xo3oo3oo *b3oo .. ..&#x ♦  8  1 |  24   8  0 |  32  24   0   0 |   8   8   32    0   0   0 |  1   0   8   8    0   0   0   0 |  *  * 120   *   *   *   *   *   *  *  * | 0  1  1   0  0  0 0
xo3oo .. *b3oo3oo ..&#x ♦  5  1 |  10   5  0 |  10  10   0   0 |   0   5   10    0   0   0 |  0   1   0   5    0   0   0   0 |  *  *   * 192   *   *   *   *   *  *  * | 0  1  0   0  1  0 0
xo3oo3oo    .. .. ox&#x ♦  4  2 |   6   8  1 |   4  12   4   0 |   1   0    8    6   0   0 |  0   0   2   0    4   0   0   0 |  *  *   *   * 480   *   *   *   *  *  * | 0  0  1   1  0  0 0
xo3oo .. *b3oo .. ox&#x ♦  4  2 |   6   8  1 |   4  12   4   0 |   0   1    8    6   0   0 |  0   0   0   2    4   0   0   0 |  *  *   *   *   * 480   *   *   *  *  * | 0  0  1   0  1  0 0
xo3oo ..    .. oo3ox&#x ♦  3  3 |   3   9  3 |   1   9   9   1 |   0   0    3    9   3   0 |  0   0   0   0    3   3   0   0 |  *  *   *   *   *   * 640   *   *  *  * | 0  0  0   1  1  0 0
xo .. ..    oo3oo3ox&#x ♦  2  4 |   1   8  6 |   0   4  12   4 |   0   0    0    6   8   1 |  0   0   0   0    0   4   2   0 |  *  *   *   *   *   *   * 240   *  *  * | 0  0  0   0  2  0 0
.. oo .. *b3oo3oo3ox&#x ♦  1  5 |   0   5 10 |   0   0  10  10 |   0   0    0    0  10   5 |  0   0   0   0    0   0   5   1 |  *  *   *   *   *   *   *   * 192  *  * | 0  0  0   0  1  1 0
.o3.o .. *b3.o3.o3.x    ♦  0  6 |   0   0 15 |   0   0   0  20 |   0   0    0    0   0  15 |  0   0   0   0    0   0   0   6 |  *  *   *   *   *   *   *   *   * 32  * | 0  0  0   0  1  0 1
.. .o3.o *b3.o3.o3.x    ♦  0  6 |   0   0 15 |   0   0   0  20 |   0   0    0    0   0  15 |  0   0   0   0    0   0   0   6 |  *  *   *   *   *   *   *   *   *  * 32 | 0  0  0   0  0  1 1
------------------------+-------+------------+-----------------+---------------------------+---------------------------------+-----------------------------------------+--------------------
x.3o.3o. *b3o.3o.3o.    ♦ 32  0 | 240   0  0 | 640   0   0   0 | 160 480    0    0   0   0 | 60 192   0   0    0   0   0   0 | 12 32   0   0   0   0   0   0   0  0  0 | 1  *  *   *  *  * *
xo3oo3oo *b3oo3oo ..&#x ♦ 16  1 |  80  16  0 | 160  80   0   0 |  40  80  160    0   0   0 | 10  16  40  80    0   0   0   0 |  1  0  10  16   0   0   0   0   0  0  0 | * 12  *   *  *  * *
xo3oo3oo *b3oo .. ox&#x ♦  8  2 |  24  16  1 |  32  48   8   0 |   8   8   64   24   0   0 |  1   0  16  16   32   0   0   0 |  0  0   2   0   8   8   0   0   0  0  0 | *  * 60   *  *  * *
xo3oo3oo    .. oo3ox&#x ♦  4  3 |   6  12  3 |   4  18  12   1 |   1   0   12   18   4   0 |  0   0   3   0   12   6   0   0 |  0  0   0   0   3   0   4   0   0  0  0 | *  *  * 160  *  * *
xo3oo .. *b3oo3oo3ox&#x ♦  6  6 |  15  30 15 |  20  60  60  20 |   0  15   60   90  60  15 |  0   6   0  30   60  60  30   6 |  0  1   0   6   0  15  20  15   6  1  0 | *  *  *   * 32  * *
.. oo3oo *b3oo3oo3ox&#x ♦  1  6 |   0   6 15 |   0   0  15  20 |   0   0    0    0  20  15 |  0   0   0   0    0   0  15   6 |  0  0   0   0   0   0   0   0   6  0  1 | *  *  *   *  * 32 *
.o3.o3.o *b3.o3.o3.x    ♦  0 12 |   0   0 60 |   0   0   0 160 |   0   0    0    0   0 240 |  0   0   0   0    0   0   0 192 |  0  0   0   0   0   0   0   0   0 32 32 | *  *  *   *  *  * 1

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