Acronym haxpy
Name hemihexeractic pyramid,
vertex pyramid of laq
Circumradius 1
Coordinates
  1. (0, 0, 0, 0, 0, 0; 1/2)
    tip
  2. (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 0)   & even permutations and even changes of sign in all but last coord.
    base
Confer
uniform relative:
laq  
general polytopal classes:
segmentoexa   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

ox3oo3oo *b3oo3oo3oo&#x   → height = 1/2

o.3o.3o. *b3o.3o.3o.    | 1  *  32   0 | 240   0 | 640   0   0 | 160 480  0   0 | 60 192  0  0 | 12 32 0
.o3.o3.o *b3.o3.o3.o    | * 32   1  15 |  15  60 |  60  20  60 |  20  60 15  30 | 15  30  6  6 |  6  6 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
oo3oo3oo *b3oo3oo3oo&#x | 1  1 | 32   *   15   0 |  60   0   0 |  20  60  0   0 | 15  30  0  0 |  6  6 0
.x .. ..    .. .. ..    | 0  2 |  * 240    1   8 |   8   4  12 |   4  12  6   8 |  6   8  4  2 |  4  2 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
ox .. ..    .. .. ..&#x | 1  2 |  2   1 | 240   *    8   0   0 |   4  12  0   0 |  6   8  0  0 |  4  2 0
.x3.o ..    .. .. ..    | 0  3 |  0   3 |   * 640 |   1   1   3 |   1   3  3   3 |  3   3  3  1 |  3  1 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
ox3oo ..    .. .. ..&#x  1  3 |  3   3 |   3   1 | 640   *   * |   1   3  0   0 |  3   3  0  0 |  3  1 0
.x3.o3.o    .. .. ..     0  4 |  0   6 |   0   4 |   * 160   * |   1   0  3   0 |  3   0  3  0 |  3  0 1
.x3.o .. *b3.o .. ..     0  4 |  0   6 |   0   4 |   *   * 480 |   0   1  1   2 |  1   2  2  1 |  2  1 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
ox3oo3oo    .. .. ..&#x  1  4 |  4   6 |   6   4 |   4   1   0 | 160   *  *   * |  3   0  0  0 |  3  0 0
ox3oo .. *b3oo .. ..&#x  1  4 |  4   6 |   6   4 |   4   0   1 |   * 480  *   * |  1   2  0  0 |  2  1 0
.x3.o3.o *b3.o .. ..     0  8 |  0  24 |   0  32 |   0   8   8 |   *   * 60   * |  1   0  2  0 |  2  0 1
.x3.o .. *b3.o3.o ..     0  5 |  0  10 |   0  10 |   0   0   5 |   *   *  * 192 |  0   1  1  1 |  1  1 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
ox3oo3oo *b3oo .. ..&#x  1  8 |  8  24 |  24  32 |  32   8   8 |   8   8  1   0 | 60   *  *  * |  2  0 0
ox3oo .. *b3oo3oo ..&#x  1  5 |  5  10 |  10  10 |  10   0   5 |   0   5  0   1 |  * 192  *  * |  1  1 0
.x3.o3.o *b3.o3.o ..     0 16 |  0  80 |   0 160 |   0  40  80 |   0   0 10  16 |  *   * 12  * |  1  0 1
.x3.o .. *b3.o3.o3.o     0  6 |  0  15 |   0  20 |   0   0  15 |   0   0  0   6 |  *   *  * 32 |  0  1 1
------------------------+------+--------+---------+-------------+----------------+--------------+--------
ox3oo3oo *b3oo3oo ..&#x  1 16 | 16  80 |  80 160 | 160  40  80 |  40  80 10  16 | 10  16  1  0 | 12  * *
ox3oo .. *b3oo3oo3oo&#x  1  6 |  6  15 |  15  20 |  20   0  15 |   0  15  0   6 |  0   6  0  1 |  * 32 *
.x3.o3.o *b3.o3.o3.o     0 32 |  0 240 |   0 640 |   0 160 480 |   0   0 60 192 |  0   0 12 32 |  *  * 1

oxo3ooo3oox oxo3ooo3oox&#x   → height(1,2) = height(1,3) = 1/2
                               height(2,3) = 0
(pt || tegum sum of 2 mutually bigyrated tetdips)

o..3o..3o.. o..3o..3o..      | 1  *  32  0   0 | 96 144  0   0 | 64 576  0   0   0   0 | 16 192 144 288  0   0  0 | 24 192 36  0  0 | 12 32 0
.o.3.o.3.o. .o.3.o.3.o.    & | * 32   1  6   9 |  6   9  6  54 |  6  54  2  24  18  36 |  2  24  18  36  6  30  9 |  6  30  9  6  6 |  6  6 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
oo.3oo.3oo. oo.3oo.3oo.&#x & | 1  1 | 32  *   *   6   9  0   0 |  6  54  0   0   0   0 |  2  24  18  36  0   0  0 |  6  30  9  0  0 |  6  6 0
.x. ... ... ... ... ...    & | 0  2 |  * 96   *   1   0  2   6 |  2   6  1   6   3   6 |  1   6   3   6  3   8  3 |  3   8  3  4  2 |  4  2 1
.oo3.oo3.oo .oo3.oo3.oo&#x   | 0  2 |  *  * 144   0   1  0   8 |  0   8  0   4   4   8 |  0   4   4   8  2   8  4 |  2   8  4  4  2 |  4  2 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
ox. ... ... ... ... ...&#x & | 1  2 |  2  1   0 | 96   *  *   *   2   6  0   0   0   0 |  1   6   3   6  0   0  0 |  3   8  3  0  0 |  4  2 0
ooo3ooo3ooo ooo3ooo3ooo&#x   | 1  2 |  2  0   1 |  * 144  *   *   0   8  0   0   0   0 |  0   4   4   8  0   0  0 |  2   8  4  0  0 |  4  2 0
.x.3.o. ... ... ... ...    & | 0  3 |  0  3   0 |  *   * 64   * |  1   0  1   3   0   0 |  1   3   0   0  3   3  0 |  3   3  0  3  1 |  3  1 1
.xo ... ... ... ... ...&#x & | 0  3 |  0  1   2 |  *   *  * 576 |  0   1  0   1   1   2 |  0   1   1   2  1   3  2 |  1   3  2  3  1 |  3  1 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
ox.3oo. ... ... ... ...&#x &  1  3 |  3  3   0 |  3   0  1   0 | 64   *  *   *   *   * |  1   3   0   0  0   0  0 |  3   3  0  0  0 |  3  1 0
oxo ... ... ... ... ...&#x &  1  3 |  3  1   2 |  1   2  0   1 |  * 576  *   *   *   * |  0   1   1   2  0   0  0 |  1   3  2  0  0 |  3  1 0
.x.3.o.3.o. ... ... ...    &  0  4 |  0  6   0 |  0   0  4   0 |  *   * 16   *   *   * |  1   0   0   0  3   0  0 |  3   0  0  3  0 |  3  0 1
.xo3.oo ... ... ... ...&#x &  0  4 |  0  3   3 |  0   0  1   3 |  *   *  * 192   *   * |  0   1   0   0  1   2  0 |  1   2  0  2  1 |  2  1 1
.xo ... .ox ... ... ...&#x &  0  4 |  0  2   4 |  0   0  0   4 |  *   *  *   * 144   * |  0   0   1   0  1   0  2 |  1   0  2  3  0 |  3  0 1
.xo ... ... ... ... .ox&#x &  0  4 |  0  2   4 |  0   0  0   4 |  *   *  *   *   * 288 |  0   0   0   1  0   2  1 |  0   2  1  2  1 |  2  1 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
ox.3oo.3oo. ... ... ...&#x &  1  4 |  4  6   0 |  6   0  4   0 |  4   0  1   0   0   0 | 16   *   *   *  *   *  * |  3   0  0  0  0 |  3  0 0
oxo3ooo ... ... ... ...&#x &  1  4 |  4  3   3 |  3   3  1   3 |  1   3  0   1   0   0 |  * 192   *   *  *   *  * |  1   2  0  0  0 |  2  1 0
oxo ... oox ... ... ...&#x &  1  4 |  4  2   4 |  2   4  0   4 |  0   4  0   0   1   0 |  *   * 144   *  *   *  * |  1   0  2  0  0 |  3  0 0
oxo ... ... ... ... oox&#x &  1  4 |  4  2   4 |  2   4  0   4 |  0   4  0   0   0   1 |  *   *   * 288  *   *  * |  0   2  1  0  0 |  2  1 0
.xo3.oo3.ox ... ... ...&#x &  0  8 |  0 12  12 |  0   0  8  24 |  0   0  2   8   6   0 |  *   *   *   * 24   *  * |  1   0  0  2  0 |  2  0 1
.xo3.oo ... ... ... .ox&#x &  0  5 |  0  4   6 |  0   0  1   9 |  0   0  0   2   0   3 |  *   *   *   *  * 192  * |  0   1  0  1  1 |  1  1 1
.xo ... .ox .xo ... .ox&#zx   0  8 |  0  8  16 |  0   0  0  32 |  0   0  0   0   8   8 |  *   *   *   *  *   * 36 |  0   0  1  2  0 |  2  0 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
oxo3ooo3oox ... ... ...&#x &  1  8 |  8 12  12 | 12  12  8  24 |  8  24  2   8   6   0 |  2   8   6   0  1   0  0 | 24   *  *  *  * |  2  0 0
oxo3ooo ... ... ... oox&#x &  1  5 |  5  4   6 |  4   6  1   9 |  1   9  0   2   0   3 |  0   2   0   3  0   1  0 |  * 192  *  *  * |  1  1 0
oxo ... oox oxo ... oox&#x    1  8 |  8  8  16 |  8  16  0  32 |  0  32  0   0   8   8 |  0   0   8   8  0   0  1 |  *   * 36  *  * |  2  0 0
.xo3.oo3.ox .xo ... .ox&#zx   0 16 |  0 32  48 |  0   0 16 144 |  0   0  4  32  36  48 |  0   0   0   0  4  16  6 |  *   *  * 12  * |  1  0 1
.xo3.oo ... ... .oo3.ox&#x &  0  6 |  0  6   9 |  0   0  2  18 |  0   0  0   6   0   9 |  0   0   0   0  0   6  0 |  *   *  *  * 32 |  0  1 1
-----------------------------+------+-----------+---------------+-----------------------+--------------------------+-----------------+--------
oxo3ooo3oox oxo ... oox&#x &  1 16 | 16 32  48 | 32  48 16 144 | 16 144  4  32  36  48 |  4  32  36  48  4  16  6 |  4  16  6  1  0 | 12  * *
oxo3ooo ... ... ooo3oox&#x &  1  6 |  6  6   9 |  6   9  2  18 |  2  18  0   6   0   9 |  0   6   0   9  0   6  0 |  0   6  0  0  1 |  * 32 *
.xo3.oo3.ox .xo3.oo3.ox&#zx   0 32 |  0 96 144 |  0   0 64 576 |  0   0 16 192 144 288 |  0   0   0   0 24 192 36 |  0   0  0 12 32 |  *  * 1

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