Acronym haxesc
Name (degenerate) demihexaractic scalene,
line atop fully orthogonal demihexaract
Circumradius ∞   i.e. flat in euclidean space

The hull of this degenerate shape is haxt. In fact, the latter provides 2 different decompositions, either into 12 hinscs plus 32 ocas (kind in the sense of a 7D orange) or equatorially into 2 haxpies. The blend of these 2 decompositions, blending out right those haxt cells each, then would result in haxesc again.

In fact, it is only this degeneracy, which lets become here the hull of a scalene to be a mere bipyramid.


Incidence matrix according to Dynkin symbol

xo ox3oo3oo *c3oo3oo3oo&#x   → height = 0
(line || perp hax)

o. o.3o.3o. *c3o.3o.3o.    | 2  *  1 32   0 | 32 240   0 | 240  640   0   0 | 640 160 480  0   0 | 160 480  60 192  0  0 | 60 192 12 32 0 | 12 32 1
.o .o3.o3.o *c3.o3.o3.o    | * 32  0  2  15 |  1  30  60 |  15  120  20  60 |  60  40 120 15  30 |  20  60  30  60  6  6 | 15  30 12 12 1 |  6  6 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
x. .. .. ..    .. .. ..    | 2  0 | 1  *   *  32   0   0 | 240    0   0   0 | 640   0   0  0   0 | 160 480   0   0  0  0 | 60 192  0  0 0 | 12 32 0
oo oo3oo3oo *c3oo3oo3oo&#x | 1  1 | * 64   *   1  15   0 |  15   60   0   0 |  60  20  60  0   0 |  20  60  15  30  0  0 | 15  30  6  6 0 |  6  6 1
.. .x .. ..    .. .. ..    | 0  2 | *  * 240   0   2   8 |   1   16   4  12 |   8   8  24  6   8 |   4  12  12  16  4  2 |  6   8  8  4 1 |  4  2 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo .. .. ..    .. .. ..&#x | 2  1 | 1  2   0 | 32   *   *   15    0   0   0 |  60   0   0  0   0 |  20  60   0   0  0  0 | 15  30  0  0 0 |  6  6 0
.. ox .. ..    .. .. ..&#x | 1  2 | 0  2   1 |  * 480   *    1    8   0   0 |   8   4  12  0   0 |   4  12   6   8  0  0 |  6   8  4  2 0 |  4  2 1
.. .x3.o ..    .. .. ..    | 0  3 | 0  0   3 |  *   * 640 |   0    2   1   3 |   1   2   6  3   3 |   1   3   6   6  3  1 |  3   3  6  2 1 |  3  1 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo ox .. ..    .. .. ..&#x  2  2 | 1  4   1 |  2   2   0 | 240    *   *   *    8   0   0  0   0 |   4  12   0   0  0  0 |  6   8  0  0 0 |  4  2 0
.. ox3oo ..    .. .. ..&#x  1  3 | 0  3   3 |  0   3   1 |   * 1280   *   * |   1   1   3  0   0 |   1   3   3   3  0  0 |  3   3  3  1 0 |  3  1 1
.. .x3.o3.o    .. .. ..     0  4 | 0  0   6 |  0   0   4 |   *    * 160   * |   0   2   0  3   0 |   1   0   6   0  3  0 |  3   0  6  0 1 |  3  0 2
.. .x3.o .. *c3.o .. ..     0  4 | 0  0   6 |  0   0   4 |   *    *   * 480 |   0   0   2  1   2 |   0   1   2   4  2  1 |  1   2  4  2 1 |  2  1 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo ox3oo ..    .. .. ..&#x  2  3 | 1  6   3 |  3   6   1 |   3    2   0   0 | 640   *   *  *   * |   1   3   0   0  0  0 |  3   3  0  0 0 |  3  1 0
.. ox3oo3oo    .. .. ..&#x  1  4 | 0  4   6 |  0   6   4 |   0    4   1   0 |   * 320   *  *   * |   1   0   3   0  0  0 |  3   0  3  0 0 |  3  0 1
.. ox3oo .. *c3oo .. ..&#x  1  4 | 0  4   6 |  0   6   4 |   0    4   0   1 |   *   * 960  *   * |   0   1   1   2  0  0 |  1   2  2  1 0 |  2  1 1
.. .x3.o3.o *c3.o .. ..     0  8 | 0  0  24 |  0   0  32 |   0    0   8   8 |   *   *   * 60   * |   0   0   2   0  2  0 |  1   0  4  0 1 |  2  0 2
.. .x3.o .. *c3.o3.o ..     0  5 | 0  0  10 |  0   0  10 |   0    0   0   5 |   *   *   *  * 192 |   0   0   0   2  1  1 |  0   1  2  2 1 |  1  1 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo ox3oo3oo    .. .. ..&#x  2  4 | 1  8   6 |  4  12   4 |   6    8   1   0 |   4   2   0  0   0 | 160   *   *   *  *  * |  3   0  0  0 0 |  3  0 0
xo ox3oo .. *c3oo .. ..&#x  2  4 | 1  8   6 |  4  12   4 |   6    8   0   1 |   4   0   2  0   0 |   * 480   *   *  *  * |  1   2  0  0 0 |  2  1 0
.. ox3oo3oo *c3oo .. ..&#x  1  8 | 0  8  24 |  0  24  32 |   0   32   8   8 |   0   8   8  1   0 |   *   * 120   *  *  * |  1   0  2  0 0 |  2  0 1
.. ox3oo .. *c3oo3oo ..&#x  1  5 | 0  5  10 |  0  10  10 |   0   10   0   5 |   0   0   5  0   1 |   *   *   * 384  *  * |  0   1  1  1 0 |  1  1 1
.. .x3.o3.o *c3.o3.o ..     0 16 | 0  0  80 |  0   0 160 |   0    0  40  80 |   0   0   0 10  16 |   *   *   *   * 12  * |  0   0  2  0 1 |  1  0 2
.. .x3.o .. *c3.o3.o3.o     0  6 | 0  0  15 |  0   0  20 |   0    0   0  15 |   0   0   0  0   6 |   *   *   *   *  * 32 |  0   0  0  2 1 |  0  1 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo ox3oo3oo *c3oo .. ..&#x  2  8 | 1 16  24 |  8  48  32 |  24   64   8   8 |  32  16  16  1   0 |   8   8   2   0  0  0 | 60   *  *  * * |  2  0 0
xo ox3oo .. *c3oo3oo ..&#x  2  5 | 1 10  10 |  5  20  10 |  10   20   0   5 |  10   0  10  0   1 |   0   5   0   2  0  0 |  * 192  *  * * |  1  1 0
.. ox3oo3oo *c3oo3oo ..&#x  1 16 | 0 16  80 |  0  80 160 |   0  160  40  80 |   0  40  80 10  16 |   0   0  10  16  1  0 |  *   * 24  * * |  1  0 1
.. ox3oo .. *c3oo3oo3oo&#x  1  6 | 0  6  15 |  0  15  20 |   0   20   0  15 |   0   0  15  0   6 |   0   0   0   6  0  1 |  *   *  * 64 * |  0  1 1
.. .x3.o3.o *c3.o3.o3.o     0 32 | 0  0 240 |  0   0 640 |   0    0 160 480 |   0   0   0 60 192 |   0   0   0   0 12 32 |  *   *  *  * 1 |  0  0 2
---------------------------+------+----------+------------+------------------+--------------------+-----------------------+----------------+--------
xo ox3oo3oo *c3oo3oo ..&#x  2 16 | 1 32  80 | 16 160 160 |  80  320  40  80 | 160  80 160 10  16 |  40  80  20  32  1  0 | 10  16  2  0 0 | 12  * *
xo ox3oo .. *c3oo3oo3oo&#x  2  6 | 1 12  15 |  6  30  20 |  15   40   0  15 |  20   0  30  0   6 |   0  15   0  12  0  1 |  0   6  0  2 0 |  * 32 *
.. ox3oo3oo *c3oo3oo3oo&#x  1 32 | 0 32 240 |  0 240 640 |   0  640 160 480 |   0 160 480 60 192 |   0   0  60 192 12 32 |  0   0 12 32 1 |  *  * 2

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