Acronym ... Name point || pseudo hax || gee,Dutour polyexon type A Lace cityin approx. ASCII-art ```o where: H H = x3o3o *b3o3o (hin) T o h = o3o3x *b3o3o (alternate hin) h T = o3o3o *b3o3x (tac) o o = o3o3o *b3o3o (point) | | + o3o3o *b3o3o3o (point) | +---- x3o3o *b3o3o3o (hax) +-------- o3o3o *b3o3o3x (gee) ``` Coordinates (0, 0, 0, 0, 0, 0, 1/sqrt(2)) (right layer of single vertex) (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. (medial hax layer) (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) Confer related segmentoexa: haxpy   gahax   general polytopal classes: Dutour's Delone cells

This polyexon is nothing but an external blend of haxpy and gahax, adjoining at an hax. There it just happens that the dihedral angle between the hinpies becomes flat, i.e. they join into an hint each.

Incidence matrix according to Dynkin symbol

```oxo3ooo3ooo *b3ooo3ooo3oox&#xt   → both heights = 1/2
(pt || (pseudo) hax || gee)

o..3o..3o.. *b3o..3o..3o..     | 1  *  * ♦ 32   0   0  0 | 240   0   0   0   0 | 640   0   0    0    0   0   0 | 160 480  0   0   0   0    0   0   0   0 | 60 192  0   0   0   0   0   0   0   0  0  0 | 12 32  0   0  0  0 0
.o.3.o.3.o. *b3.o.3.o.3.o.     | * 32  * |  1  15   6  0 |  15  60  60  15   0 |  60  20  60  180   90  20   0 |  20  60 15  30  60 120  180  60  15   0 |  0  30  6  30  30  60  60  60  15   6  0  0 |  6  6 15  20  6  1 0
..o3..o3..o *b3..o3..o3..o     | *  * 12 ♦  0   0  16 10 |   0   0  80  80  40 |   0   0   0  160  240 160  80 |   0   0  0   0  40  80  320 240 160  80 |  0   0  0  10  16  80  80 160  60  80 16 16 |  1  0 10  40 16 16 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
oo.3oo.3oo. *b3oo.3oo.3oo.&#x  | 1  1  0 | 32   *   *  * ♦  15   0   0   0   0 |  60   0   0    0    0   0   0 |  20  60  0   0   0   0    0   0   0   0 | 15  30  0   0   0   0   0   0   0   0  0  0 |  6  6  0   0  0  0 0
.x. ... ...    ... ... ...     | 0  2  0 |  * 240   *  * |   1   8   4   0   0 |   8   4  12   24    6   0   0 |   4  12  6   8  12  24   24   4   0   0 |  6   8  2  12   8  12  12   8   1   0  0  0 |  4  2  6   4  2  0 0
.oo3.oo3.oo *b3.oo3.oo3.oo&#x  | 0  1  1 |  *   * 192  * |   0   0  10   5   0 |   0   0   0   30   30  10   0 |   0   0  0   0  10  20   60  30  10   0 |  0   0  0   5   5  20  20  30  10   5  0  0 |  1  0  5  10  5  1 0
... ... ...    ... ... ..x     | 0  0  2 |  *   *   * 60 ♦   0   0   0   8   8 |   0   0   0    0   24  32  24 |   0   0  0   0   0   0   32  48  48  32 |  0   0  0   0   0   8   8  32  24  32  8  8 |  0  0  1   8  8  8 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
ox. ... ...    ... ... ...&#x  | 1  2  0 |  2   1   0  0 | 240   *   *   *   * ♦   8   0   0    0    0   0   0 |   4  12  0   0   0   0    0   0   0   0 |  6   8  0   0   0   0   0   0   0   0  0  0 |  4  2  0   0  0  0 0
.x.3.o. ...    ... ... ...     | 0  3  0 |  0   3   0  0 |   * 640   *   *   * |   1   1   3    3    0   0   0 |   1   3  3   3   3   6    3   0   0   0 |  3   3  1   6   3   3   3   1   0   0  0  0 |  3  1  3   1  1  0 0
.xo ... ...    ... ... ...&#x  | 0  2  1 |  0   1   2  0 |   *   * 960   *   * |   0   0   0    6    3   0   0 |   0   0  0   0   3   6   12   3   0   0 |  0   0  0   3   2   6   6   6   1   0  0  0 |  1  0  3   3  2  0 0
... ... ...    ... ... .ox&#x  | 0  1  2 |  0   0   2  1 |   *   *   * 480   * |   0   0   0    0    6   4   0 |   0   0  0   0   0   0   12  12   6   0 |  0   0  0   0   0   4   4  12   6   4  0  0 |  0  0  1   4  4  1 0
... ... ...    ... ..o3..x     | 0  0  3 |  0   0   0  3 |   *   *   *   * 160 ♦   0   0   0    0    0   4   6 |   0   0  0   0   0   0    0   6  12  12 |  0   0  0   0   0   0   0   4   6  12  4  4 |  0  0  0   1  4  4 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
ox.3oo. ...    ... ... ...&#x  ♦ 1  3  0 |  3   3   0  0 |   3   1   0   0   0 | 640   *   *    *    *   *   * |   1   3  0   0   0   0    0   0   0   0 |  3   3  0   0   0   0   0   0   0   0  0  0 |  3  1  0   0  0  0 0
.x.3.o.3.o.    ... ... ...     ♦ 0  4  0 |  0   6   0  0 |   0   4   0   0   0 |   * 160   *    *    *   *   * |   1   0  3   0   3   0    0   0   0   0 |  3   0  0   6   0   3   0   0   0   0  0  0 |  3  0  3   1  0  0 0
.x.3.o. ... *b3.o. ... ...     ♦ 0  4  0 |  0   6   0  0 |   0   4   0   0   0 |   *   * 480    *    *   *   * |   0   1  1   2   0   2    0   0   0   0 |  1   2  1   2   2   0   1   0   0   0  0  0 |  2  1  1   0  1  0 0
.xo3.oo ...    ... ... ...&#x  ♦ 0  3  1 |  0   3   3  0 |   0   1   3   0   0 |   *   *   * 1920    *   *   * |   0   0  0   0   1   2    2   0   0   0 |  0   0  0   2   1   2   2   1   0   0  0  0 |  1  0  2   1  1  0 0
.xo ... ...    ... ... .ox&#x  ♦ 0  2  2 |  0   1   4  1 |   0   0   2   2   0 |   *   *   *    * 1440   *   * |   0   0  0   0   0   0    4   2   0   0 |  0   0  0   0   0   2   2   4   1   0  0  0 |  0  0  1   2  2  0 0
... ... ...    ... .oo3.ox&#x  ♦ 0  1  3 |  0   0   3  3 |   0   0   0   3   1 |   *   *   *    *    * 640   * ♦   0   0  0   0   0   0    0   3   3   0 |  0   0  0   0   0   0   0   3   3   3  0  0 |  0  0  0   1  3  1 0
... ... ...    ..o3..o3..x     ♦ 0  0  4 |  0   0   0  6 |   0   0   0   0   4 |   *   *   *    *    *   * 240 ♦   0   0  0   0   0   0    0   0   2   4 |  0   0  0   0   0   0   0   0   1   4  2  2 |  0  0  0   0  2  2 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
ox.3oo.3oo.    ... ... ...&#x  ♦ 1  4  0 |  4   6   0  0 |   6   4   0   0   0 |   4   1   0    0    0   0   0 | 160   *  *   *   *   *    *   *   *   * |  3   0  0   0   0   0   0   0   0   0  0  0 |  3  0  0   0  0  0 0
ox.3oo. ... *b3oo. ... ...&#x  ♦ 1  4  0 |  4   6   0  0 |   6   4   0   0   0 |   4   0   1    0    0   0   0 |   * 480  *   *   *   *    *   *   *   * |  1   2  0   0   0   0   0   0   0   0  0  0 |  2  1  0   0  0  0 0
.x.3.o.3.o. *b3.o. ... ...     ♦ 0  8  0 |  0  24   0  0 |   0  32   0   0   0 |   0   8   8    0    0   0   0 |   *   * 60   *   *   *    *   *   *   * |  1   0  0   2   0   0   0   0   0   0  0  0 |  2  0  1   0  0  0 0
.x.3.o. ... *b3.o.3.o. ...     ♦ 0  5  0 |  0  10   0  0 |   0  10   0   0   0 |   0   0   5    0    0   0   0 |   *   *  * 192   *   *    *   *   *   * |  0   1  1   0   1   0   0   0   0   0  0  0 |  1  1  0   0  1  0 0
.xo3.oo3.oo    ... ... ...&#x  ♦ 0  4  1 |  0   6   4  0 |   0   4   6   0   0 |   0   1   0    4    0   0   0 |   *   *  *   * 480   *    *   *   *   * |  0   0  0   2   0   2   0   0   0   0  0  0 |  1  0  2   1  0  0 0
.xo3.oo ... *b3.oo ... ...&#x  ♦ 0  4  1 |  0   6   4  0 |   0   4   6   0   0 |   0   0   1    4    0   0   0 |   *   *  *   *   * 960    *   *   *   * |  0   0  0   1   1   0   1   0   0   0  0  0 |  1  0  1   0  1  0 0
.xo3.oo ...    ... ... .ox&#x  ♦ 0  3  2 |  0   3   6  1 |   0   1   6   3   0 |   0   0   0    2    3   0   0 |   *   *  *   *   *   * 1920   *   *   * |  0   0  0   0   0   1   1   1   0   0  0  0 |  0  0  1   1  1  0 0
.xo ... ...    ... .oo3.ox&#x  ♦ 0  2  3 |  0   1   6  3 |   0   0   3   6   1 |   0   0   0    0    3   2   0 |   *   *  *   *   *   *    * 960   *   * |  0   0  0   0   0   0   0   2   1   0  0  0 |  0  0  0   1  2  0 0
... ... ...    .oo3.oo3.ox&#x  ♦ 0  1  4 |  0   0   4  6 |   0   0   0   6   4 |   0   0   0    0    0   4   1 |   *   *  *   *   *   *    *   * 480   * |  0   0  0   0   0   0   0   0   1   2  0  0 |  0  0  0   0  2  1 0
... ..o ... *b3..o3..o3..x     ♦ 0  0  5 |  0   0   0 10 |   0   0   0   0  10 |   0   0   0    0    0   0   5 |   *   *  *   *   *   *    *   *   * 192 |  0   0  0   0   0   0   0   0   0   1  1  1 |  0  0  0   0  1  1 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
ox.3oo.3oo. *b3oo. ... ...&#x  ♦ 1  8  0 |  8  24   0  0 |  24  32   0   0   0 |  32   8   8    0    0   0   0 |   8   8  1   0   0   0    0   0   0   0 | 60   *  *   *   *   *   *   *   *   *  *  * |  2  0  0   0  0  0 0
ox.3oo. ... *b3oo.3oo. ...&#x  ♦ 1  5  0 |  5  10   0  0 |  10  10   0   0   0 |  10   0   5    0    0   0   0 |   0   5  0   1   0   0    0   0   0   0 |  * 192  *   *   *   *   *   *   *   *  *  * |  1  1  0   0  0  0 0
.x.3.o. ... *b3.o.3.o.3.o.     ♦ 0  6  0 |  0  15   0  0 |   0  20   0   0   0 |   0   0  15    0    0   0   0 |   0   0  0   6   0   0    0   0   0   0 |  *   * 32   *   *   *   *   *   *   *  *  * |  0  1  0   0  1  0 0
.xo3.oo3.oo *b3.oo ... ...&#x  ♦ 0  8  1 |  0  24   8  0 |   0  32  24   0   0 |   0   8   8   32    0   0   0 |   0   0  1   0   8   8    0   0   0   0 |  *   *  * 120   *   *   *   *   *   *  *  * |  1  0  1   0  0  0 0
.xo3.oo ... *b3.oo3.oo ...&#x  ♦ 0  5  1 |  0  10   5  0 |   0  10  10   0   0 |   0   0   5   10    0   0   0 |   0   0  0   1   0   5    0   0   0   0 |  *   *  *   * 192   *   *   *   *   *  *  * |  1  0  0   0  1  0 0
.xo3.oo3.oo    ... ... .ox&#x  ♦ 0  4  2 |  0   6   8  1 |   0   4  12   4   0 |   0   1   0    8    6   0   0 |   0   0  0   0   2   0    4   0   0   0 |  *   *  *   *   * 480   *   *   *   *  *  * |  0  0  1   1  0  0 0
.xo3.oo ... *b3.oo ... .ox&#x  ♦ 0  4  2 |  0   6   8  1 |   0   4  12   4   0 |   0   0   1    8    6   0   0 |   0   0  0   0   0   2    4   0   0   0 |  *   *  *   *   *   * 480   *   *   *  *  * |  0  0  1   0  1  0 0
.xo3.oo ...    ... .oo3.ox&#x  ♦ 0  3  3 |  0   3   9  3 |   0   1   9   9   1 |   0   0   0    3    9   3   0 |   0   0  0   0   0   0    3   3   0   0 |  *   *  *   *   *   *   * 640   *   *  *  * |  0  0  0   1  1  0 0
.xo ... ...    .oo3.oo3.ox&#x  ♦ 0  2  4 |  0   1   8  6 |   0   0   4  12   4 |   0   0   0    0    6   8   1 |   0   0  0   0   0   0    0   4   2   0 |  *   *  *   *   *   *   *   * 240   *  *  * |  0  0  0   0  2  0 0
... .oo ... *b3.oo3.oo3.ox&#x  ♦ 0  1  5 |  0   0   5 10 |   0   0   0  10  10 |   0   0   0    0    0  10   5 |   0   0  0   0   0   0    0   0   5   1 |  *   *  *   *   *   *   *   *   * 192  *  * |  0  0  0   0  1  1 0
..o3..o ... *b3..o3..o3..x     ♦ 0  0  6 |  0   0   0 15 |   0   0   0   0  20 |   0   0   0    0    0   0  15 |   0   0  0   0   0   0    0   0   0   6 |  *   *  *   *   *   *   *   *   *   * 32  * |  0  0  0   0  1  0 1
... ..o3..o *b3..o3..o3..x     ♦ 0  0  6 |  0   0   0 15 |   0   0   0   0  20 |   0   0   0    0    0   0  15 |   0   0  0   0   0   0    0   0   0   6 |  *   *  *   *   *   *   *   *   *   *  * 32 |  0  0  0   0  0  1 1
-------------------------------+---------+---------------+---------------------+-------------------------------+-----------------------------------------+---------------------------------------------+---------------------
oxo3ooo3ooo *b3ooo3ooo ...&#xt ♦ 1 16  1 | 16  80  16  0 |  80 160  80   0   0 | 160  40  80  160    0   0   0 |  40  80 10  16  40  80    0   0   0   0 | 10  16  0  10  16   0   0   0   0   0  0  0 | 12  *  *   *  *  * *
ox.3oo. ... *b3oo.3oo.3oo.&#x  ♦ 1  6  0 |  6  15   0  0 |  15  20   0   0   0 |  20   0  15    0    0   0   0 |   0  15  0   6   0   0    0   0   0   0 |  0   6  1   0   0   0   0   0   0   0  0  0 |  * 32  *   *  *  * *
.xo3.oo3.oo *b3.oo ... .ox&#x  ♦ 0  8  2 |  0  24  16  1 |   0  32  48   8   0 |   0   8   8   64   24   0   0 |   0   0  1   0  16  16   32   0   0   0 |  0   0  0   2   0   8   8   0   0   0  0  0 |  *  * 60   *  *  * *
.xo3.oo3.oo    ... .oo3.ox&#x  ♦ 0  4  3 |  0   6  12  3 |   0   4  18  12   1 |   0   1   0   12   18   4   0 |   0   0  0   0   3   0   12   6   0   0 |  0   0  0   0   0   3   0   4   0   0  0  0 |  *  *  * 160  *  * *
.xo3.oo ... *b3.oo3.oo3.ox&#x  ♦ 0  6  6 |  0  15  30 15 |   0  20  60  60  20 |   0   0  15   60   90  60  15 |   0   0  0   6   0  30   60  60  30   6 |  0   0  1   0   6   0  15  20  15   6  1  0 |  *  *  *   * 32  * *
... .oo3.oo *b3.oo3.oo3.ox&#x  ♦ 0  1  6 |  0   0   6 15 |   0   0   0  15  20 |   0   0   0    0    0  20  15 |   0   0  0   0   0   0    0   0  15   6 |  0   0  0   0   0   0   0   0   0   6  0  1 |  *  *  *   *  * 32 *
..o3..o3..o *b3..o3..o3..x     ♦ 0  0 12 |  0   0   0 60 |   0   0   0   0 160 |   0   0   0    0    0   0 240 |   0   0  0   0   0   0    0   0   0 192 |  0  0   0   0   0   0   0   0   0   0 32 32 |  *  *  *   *  *  * 1
```