Acronym haxabrag Name hax-first monostratic cap of lin,hax atop brag Circumradius sqrt(7)/2 = 1.322876 Lace cityin approx. ASCII-art ``` A B a -- x3o3o *b3o3o3o (hax) B C c B -- o3o3o *b3x3o3o (brag) where: A = x3o3o3o3o (hix) a = o3o3o3o3x (dual hix) B = o3o3x3o3o (dot) C = x3o3x3o3o (spix) c = o3o3x3o3x (alt. spix) ``` ``` h H -- x3o3o *b3o3o3o (hax) r n r -- o3o3o *b3x3o3o (brag) where: h = x3o3o *b3o3o (hin) H = o3o3x *b3o3o (alt. hin) r = o3o3o *b3x3o (rat) ``` Confer uniform relative: lin   segmentoexa: bragasochax   general polytopal classes: segmentoexa   fundamental lace prisms

Incidence matrix according to Dynkin symbol

```xo3oo3oo *b3ox3oo3oo&#x   → height = 1/2
(hax || brag)

o.3o.3o. *b3o.3o.3o.    | 32   * ♦  15  20    0 |  60  60   90    0   0 |  20  60  60   90   60   60   0   0   0   0 | 15  30  20  60  60  15  30  15  0   0   0   0 |  6  6 15  30  15   6   6  0  0  0 | 1  6  6  1 0
.o3.o3.o *b3.o3.o3.o    |  * 160 |   0   4   18 |   0   6   36   36  18 |   0   0   4   18   18   18  12  12  36   6 |  0   0   1  12  18  12  36  12  3  12  12  12 |  0  0  3  12   6  12  12  3  4  4 | 0  3  4  4 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x. .. ..    .. .. ..    |  2   0 | 240   *    * ♦   8   4    0    0   0 |   4  12   8    6    0    0   0   0   0   0 |  6   8   4  12   4   0   0   0  0   0   0   0 |  4  2  6   8   1   0   0  0  0  0 | 1  4  2  0 0
oo3oo3oo *b3oo3oo3oo&#x |  1   1 |   * 640    * ♦   0   3    9    0   0 |   0   0   3    9    9    9   0   0   0   0 |  0   0   1   9   9   3   9   3  0   0   0   0 |  0  0  3   9   3   3   3  0  0  0 | 0  3  3  1 0
.. .. ..    .x .. ..    |  0   2 |   *   * 1440 |   0   0    2    4   2 |   0   0   0    1    4    4   2   2   8   1 |  0   0   0   2   2   2   8   2  1   4   4   4 |  0  0  1   4   1   4   4  2  2  2 | 0  2  2  2 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x.3o. ..    .. .. ..    |  3   0 |   3   0    0 | 640   *    *    *   * |   1   3   1    0    0    0   0   0   0   0 |  3   3   1   3   0   0   0   0  0   0   0   0 |  3  1  3   3   0   0   0  0  0  0 | 1  3  1  0 0
xo .. ..    .. .. ..&#x |  2   1 |   1   2    0 |   * 960    *    *   * |   0   0   2    3    0    0   0   0   0   0 |  0   0   1   6   3   0   0   0  0   0   0   0 |  0  0  3   6   1   0   0  0  0  0 | 0  3  2  0 0
.. .. ..    ox .. ..&#x |  1   2 |   0   2    1 |   *   * 2880    *   * |   0   0   0    1    2    2   0   0   0   0 |  0   0   0   2   2   1   4   1  0   0   0   0 |  0  0  1   4   1   2   2  0  0  0 | 0  2  2  1 0
.. .o .. *b3.x .. ..    |  0   3 |   0   0    3 |   *   *    * 1920   * |   0   0   0    0    1    0   1   1   2   0 |  0   0   0   1   0   1   2   0  1   2   2   1 |  0  0  1   2   0   2   1  2  1  1 | 0  2  1  1 1
.. .. ..    .x3.o ..    |  0   3 |   0   0    3 |   *   *    *    * 960 |   0   0   0    0    0    2   0   0   4   1 |  0   0   0   0   1   0   4   2  0   2   2   4 |  0  0  0   2   1   2   4  1  2  2 | 0  1  2  2 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x.3o.3o.    .. .. ..    ♦  4   0 |   6   0    0 |   4   0    0    0   0 | 160   *   *    *    *    *   *   *   *   * |  3   0   1   0   0   0   0   0  0   0   0   0 |  3  0  3   0   0   0   0  0  0  0 | 1  3  0  0 0
x.3o. .. *b3o. .. ..    ♦  4   0 |   6   0    0 |   4   0    0    0   0 |   * 480   *    *    *    *   *   *   *   * |  1   2   0   1   0   0   0   0  0   0   0   0 |  2  1  1   2   0   0   0  0  0  0 | 1  2  1  0 0
xo3oo ..    .. .. ..&#x ♦  3   1 |   3   3    0 |   1   3    0    0   0 |   *   * 640    *    *    *   *   *   *   * |  0   0   1   3   0   0   0   0  0   0   0   0 |  0  0  3   3   0   0   0  0  0  0 | 0  3  1  0 0
xo .. ..    ox .. ..&#x ♦  2   2 |   1   4    1 |   0   2    2    0   0 |   *   *   * 1440    *    *   *   *   *   * |  0   0   0   2   2   0   0   0  0   0   0   0 |  0  0  1   4   1   0   0  0  0  0 | 0  2  2  0 0
.. oo .. *b3ox .. ..&#x ♦  1   3 |   0   3    3 |   0   0    3    1   0 |   *   *   *    * 1920    *   *   *   *   * |  0   0   0   1   0   1   2   0  0   0   0   0 |  0  0  1   2   0   2   1  0  0  0 | 0  2  1  1 0
.. .. ..    ox3oo ..&#x ♦  1   3 |   0   3    3 |   0   0    3    0   1 |   *   *   *    *    * 1920   *   *   *   * |  0   0   0   0   1   0   2   1  0   0   0   0 |  0  0  0   2   1   1   2  0  0  0 | 0  1  2  1 0
.o3.o .. *b3.x .. ..    ♦  0   4 |   0   0    6 |   0   0    0    4   0 |   *   *   *    *    *    * 480   *   *   * |  0   0   0   1   0   0   0   0  1   2   0   0 |  0  0  1   2   0   0   0  2  1  0 | 0  2  1  0 1
.. .o3.o *b3.x .. ..    ♦  0   4 |   0   0    6 |   0   0    0    4   0 |   *   *   *    *    *    *   * 480   *   * |  0   0   0   0   0   1   0   0  1   0   2   0 |  0  0  1   0   0   2   0  2  0  1 | 0  2  0  1 1
.. .o .. *b3.x3.o ..    ♦  0   6 |   0   0   12 |   0   0    0    4   4 |   *   *   *    *    *    *   *   * 960   * |  0   0   0   0   0   0   1   0  0   1   1   1 |  0  0  0   1   0   1   1  1  1  1 | 0  1  1  1 1
.. .. ..    .x3.o3.o    ♦  0   4 |   0   0    6 |   0   0    0    0   4 |   *   *   *    *    *    *   *   *   * 240 |  0   0   0   0   0   0   0   2  0   0   0   4 |  0  0  0   0   1   0   4  0  2  2 | 0  0  2  2 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x.3o.3o. *b3o. .. ..    ♦  8   0 |  24   0    0 |  32   0    0    0   0 |   8   8   0    0    0    0   0   0   0   0 | 60   *   *   *   *   *   *   *  *   *   *   * |  2  0  1   0   0   0   0  0  0  0 | 1  2  0  0 0
x.3o. .. *b3o.3o. ..    ♦  5   0 |  10   0    0 |  10   0    0    0   0 |   0   5   0    0    0    0   0   0   0   0 |  * 192   *   *   *   *   *   *  *   *   *   * |  1  1  0   1   0   0   0  0  0  0 | 1  1  1  0 0
xo3oo3oo    .. .. ..&#x ♦  4   1 |   6   4    0 |   4   6    0    0   0 |   1   0   4    0    0    0   0   0   0   0 |  *   * 160   *   *   *   *   *  *   *   *   * |  0  0  3   0   0   0   0  0  0  0 | 0  3  0  0 0
xo3oo .. *b3ox .. ..&#x ♦  4   4 |   6  12    6 |   4  12   12    4   0 |   0   1   4    6    4    0   1   0   0   0 |  *   *   * 480   *   *   *   *  *   *   *   * |  0  0  1   2   0   0   0  0  0  0 | 0  2  1  0 0
xo .. ..    ox3oo ..&#x ♦  2   3 |   1   6    3 |   0   3    6    0   1 |   0   0   0    3    0    2   0   0   0   0 |  *   *   *   * 960   *   *   *  *   *   *   * |  0  0  0   2   1   0   0  0  0  0 | 0  1  2  0 0
.. oo3oo *b3ox .. ..&#x ♦  1   4 |   0   4    6 |   0   0    6    4   0 |   0   0   0    0    4    0   0   1   0   0 |  *   *   *   *   * 480   *   *  *   *   *   * |  0  0  1   0   0   2   0  0  0  0 | 0  2  0  1 0
.. oo .. *b3ox3oo ..&#x ♦  1   6 |   0   6   12 |   0   0   12    4   4 |   0   0   0    0    4    4   0   0   1   0 |  *   *   *   *   *   * 960   *  *   *   *   * |  0  0  0   1   0   1   1  0  0  0 | 0  1  1  1 0
.. .. ..    ox3oo3oo&#x ♦  1   4 |   0   4    6 |   0   0    6    0   4 |   0   0   0    0    0    4   0   0   0   1 |  *   *   *   *   *   *   * 480  *   *   *   * |  0  0  0   0   1   0   2  0  0  0 | 0  0  2  1 0
.o3.o3.o *b3.x .. ..    ♦  0   8 |   0   0   24 |   0   0    0   32   0 |   0   0   0    0    0    0   8   8   0   0 |  *   *   *   *   *   *   *   * 60   *   *   * |  0  0  1   0   0   0   0  2  0  0 | 0  2  0  0 1
.o3.o .. *b3.x3.o ..    ♦  0  10 |   0   0   30 |   0   0    0   20  10 |   0   0   0    0    0    0   5   0   5   0 |  *   *   *   *   *   *   *   *  * 192   *   * |  0  0  0   1   0   0   0  1  1  0 | 0  1  1  0 1
.. .o3.o *b3.x3.o ..    ♦  0  10 |   0   0   30 |   0   0    0   20  10 |   0   0   0    0    0    0   0   5   5   0 |  *   *   *   *   *   *   *   *  *   * 192   * |  0  0  0   0   0   1   0  1  0  1 | 0  1  0  1 1
.. .o .. *b3.x3.o3.o    ♦  0  10 |   0   0   30 |   0   0    0   10  20 |   0   0   0    0    0    0   0   0   5   5 |  *   *   *   *   *   *   *   *  *   *   * 192 |  0  0  0   0   0   0   1  0  1  1 | 0  0  1  1 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x.3o.3o. *b3o.3o. ..    ♦ 16   0 |  80   0    0 | 160   0    0    0   0 |  40  80   0    0    0    0   0   0   0   0 | 10  16   0   0   0   0   0   0  0   0   0   0 | 12  *  *   *   *   *   *  *  *  * | 1  1  0  0 0
x.3o. .. *b3o.3o.3o.    ♦  6   0 |  15   0    0 |  20   0    0    0   0 |   0  15   0    0    0    0   0   0   0   0 |  0   6   0   0   0   0   0   0  0   0   0   0 |  * 32  *   *   *   *   *  *  *  * | 1  0  1  0 0
xo3oo3oo *b3ox .. ..&#x ♦  8   8 |  24  32   24 |  32  48   48   32   0 |   8   8  32   24   32    0   8   8   0   0 |  1   0   8   8   0   8   0   0  1   0   0   0 |  *  * 60   *   *   *   *  *  *  * | 0  2  0  0 0
xo3oo .. *b3ox3oo ..&#x ♦  5  10 |  10  30   30 |  10  30   60   20  10 |   0   5  10   30   20   20   5   0   5   0 |  0   1   0   5  10   0   5   0  0   1   0   0 |  *  *  * 192   *   *   *  *  *  * | 0  1  1  0 0
xo .. ..    ox3oo3oo&#x ♦  2   4 |   1   8    6 |   0   4   12    0   4 |   0   0   0    6    0    8   0   0   0   1 |  0   0   0   0   4   0   0   2  0   0   0   0 |  *  *  *   * 240   *   *  *  *  * | 0  0  2  0 0
.. oo3oo *b3ox3oo ..&#x ♦  1  10 |   0  10   30 |   0   0   30   20  10 |   0   0   0    0   20   10   0   5   5   0 |  0   0   0   0   0   5   5   0  0   0   1   0 |  *  *  *   *   * 192   *  *  *  * | 0  1  0  1 0
.. oo .. *b3ox3oo3oo&#x ♦  1  10 |   0  10   30 |   0   0   30   10  20 |   0   0   0    0   10   20   0   0   5   5 |  0   0   0   0   0   0   5   5  0   0   0   1 |  *  *  *   *   *   * 192  *  *  * | 0  0  1  1 0
.o3.o3.o *b3.x3.o ..    ♦  0  40 |   0   0  240 |   0   0    0  320  80 |   0   0   0    0    0    0  80  80  80   0 |  0   0   0   0   0   0   0   0 10  16  16   0 |  *  *  *   *   *   *   * 12  *  * | 0  1  0  0 1
.o3.o .. *b3.x3.o3.o    ♦  0  20 |   0   0   90 |   0   0    0   60  60 |   0   0   0    0    0    0  15   0  30  15 |  0   0   0   0   0   0   0   0  0   6   0   6 |  *  *  *   *   *   *   *  * 32  * | 0  0  1  0 1
.. .o3.o *b3.x3.o3.o    ♦  0  20 |   0   0   90 |   0   0    0   60  60 |   0   0   0    0    0    0   0  15  30  15 |  0   0   0   0   0   0   0   0  0   0   6   6 |  *  *  *   *   *   *   *  *  * 32 | 0  0  0  1 1
------------------------+--------+--------------+-----------------------+--------------------------------------------+-----------------------------------------------+-----------------------------------+-------------
x.3o.3o. *b3o.3o.3o.    ♦ 32   0 | 240   0    0 | 640   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  0  0  0 | 1  *  *  * 0
xo3oo3oo *b3ox3oo ..&#x ♦ 16  40 |  80 160  240 | 160 240  480  320  80 |  40  80 160  240  320  160  80  80  80   0 | 10  16  40  80  80  80  80   0 10  16  16   0 |  1  0 10  16   0  16   0  1  0  0 | * 12  *  * 0
xo3oo .. *b3ox3oo3oo&#x ♦  6  20 |  15  60   90 |  20  60  180   60  60 |   0  15  20   90   60  120  15   0  30  15 |  0   6   0  15  60   0  30  30  0   6   0   6 |  0  1  0   6  15   0   6  0  1  0 | *  * 32  * 0
.. oo3oo *b3ox3oo3oo&#x ♦  1  20 |   0  20   90 |   0   0   90   60  60 |   0   0   0    0   60   60   0  15  30  15 |  0   0   0   0   0  15  30  15  0   0   6   6 |  0  0  0   0   0   6   6  0  0  1 | *  *  * 32 0
.o3.o3.o *b3.x3.o3.o    ♦  0 160 |   0   0 1440 |   0   0    0 1920 960 |   0   0   0    0    0    0 480 480 960 240 |  0   0   0   0   0   0   0   0 60 192 192 192 |  0  0  0   0   0   0   0 12 32 32 | *  *  *  * 1
```