Acronym zahesa Name zee || hesa Circumradius 1 Lace cityin approx. ASCII-art ```o where: H H = x3o3o *b3o3o3o (hax) T h = o3o3x *b3o3o3o (alternate hax) h T = o3o3o *b3o3o3x (gee) o o = o3o3o *b3o3o3o (point) | +---- x3o3o *b3o3o3o3o (hesa) +-------- o3o3o *b3o3o3o3x (zee) ``` Coordinates (1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8); 1/sqrt(8))     & all even changes of sign in all but last coord. (hesa layer) (1/sqrt(2), 0, 0, 0, 0, 0, 0; 1/sqrt(2))     & all permutations, all changes of sign in all but last coord. (zee layer) Confer uniform relative: fy   related Delone cells: Dutour polyzetton type A   general polytopal classes: segmentozetta   fundamental lace prisms

Incidence matrix according to Dynkin symbol

```xo3oo3oo *b3oo3oo3oo3ox&#x   → height = 1/sqrt(8) = 0.353553
(hesa || zee)

o.3o.3o. *b3o.3o.3o.3o.    | 64  * |  21   7  0 |  105  105   21   0 |  35  140  420  210   35   0 |  35  105  140  420   630  210   35   0 | 21  42 105  210  210  420  420  105   21   0 |  7  7  42 105  140  42  105  140  105  21   7  0  0 | 1  7 21  35  35  7  1 0
.o3.o3.o *b3.o3.o3.o3.o    |  * 14 ♦   0  32 12 |    0  240  192  60 |   0    0  640  960  480 160 |   0    0  160  480  1920 1440  640 240 |  0   0  60  192  480  960 1920  960  480 192 |  0  0  12 120  480  32  192  480  640 240 192 32 32 | 0  1 12  60 160 32 32 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x. .. ..    .. .. .. ..    |  2  0 | 672   *  * |   10    5    0   0 |   5   20   40   10    0   0 |  10   20   20   60    60   10    0   0 | 10  10  30   40   30   60   40    5    0   0 |  5  2  20  30   20  10   20   20   10   1   0  0  0 | 1  5 10  10   5  2  0 0
oo3oo3oo *b3oo3oo3oo3oo&#x |  1  1 |   * 448  * ♦    0   15    6   0 |   0    0   60   60   15   0 |   0    0   20   60   180   90   20   0 |  0   0  15   30   60  120  180   60   15   0 |  0  0   6  30   60   6   30   60   60  15   6  0  0 | 0  1  6  15  20  6  1 0
.. .. ..    .. .. .. .x    |  0  2 |   *   * 84 ♦    0    0   16  10 |   0    0    0   80   80  40 |   0    0    0    0   160  240  160  80 |  0   0   0    0   40   80  320  240  160  80 |  0  0   0  10   80   0   16   80  160  80  80 16 16 | 0  0  1  10  40 16 16 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x.3o. ..    .. .. .. ..    |  3  0 |   3   0  0 | 2240    *    *   * |   1    4    4    0    0   0 |   4    6    4   12     6    0    0   0 |  6   4  12   12    6   12    4    0    0   0 |  4  1  12  12    4   4    6    4    1   0   0  0  0 | 1  4  6   4   1  4  0 0
xo .. ..    .. .. .. ..&#x |  2  1 |   1   2  0 |    * 3360    *   * |   0    0    8    4    0   0 |   0    0    4   12    24    6    0   0 |  0   0   6    8   12   24   24    4    0   0 |  0  0   4  12   12   2    8   12    8   1   0  0  0 | 0  1  4   6   4  2  0 0
.. .. ..    .. .. .. ox&#x |  1  2 |   0   2  1 |    *    * 1344   * ♦   0    0    0   10    5   0 |   0    0    0    0    30   30   10   0 |  0   0   0    0   10   20   60   30   10   0 |  0  0   0   5   20   0    5   20   30  10   5  0  0 | 0  0  1   5  10  5  1 0
.. .. ..    .. .. .o3.x    |  0  3 |   0   0  3 |    *    *    * 280 ♦   0    0    0    0    8   8 |   0    0    0    0     0   24   32  24 |  0   0   0    0    0    0   32   48   48  32 |  0  0   0   0    8   0    0    8   32  24  32  8  8 | 0  0  0   1   8  8  8 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x.3o.3o.    .. .. .. ..    ♦  4  0 |   6   0  0 |    4    0    0   0 | 560    *    *    *    *   * |   4    0    4    0     0    0    0   0 |  6   0  12    0    6    0    0    0    0   0 |  4  0  12  12    4   0    0    0    0   0   0  0  0 | 1  4  6   4   1  0  0 0
x.3o. .. *b3o. .. .. ..    ♦  4  0 |   6   0  0 |    4    0    0   0 |   * 2240    *    *    *   * |   1    3    0    3     0    0    0   0 |  3   3   3    6    0    3    0    0    0   0 |  3  1   6   3    0   3    3    1    0   0   0  0  0 | 1  3  3   1   0  1  0 0
xo3oo ..    .. .. .. ..&#x ♦  3  1 |   3   3  0 |    1    3    0   0 |   *    * 8960    *    *   * |   0    0    1    3     3    0    0   0 |  0   0   3    3    3    6    3    0    0   0 |  0  0   3   6    3   1    3    3    1   0   0  0  0 | 0  1  3   3   1  1  0 0
xo .. ..    .. .. .. ox&#x ♦  2  2 |   1   4  1 |    0    2    2   0 |   *    *    * 6720    *   * ♦   0    0    0    0     6    3    0   0 |  0   0   0    0    3    6   12    3    0   0 |  0  0   0   3    6   0    2    6    6   1   0  0  0 | 0  0  1   3   3  2  0 0
.. .. ..    .. .. oo3ox&#x ♦  1  3 |   0   3  3 |    0    0    3   1 |   *    *    *    * 2240   * ♦   0    0    0    0     0    6    4   0 |  0   0   0    0    0    0   12   12    6   0 |  0  0   0   0    4   0    0    4   12   6   4  0  0 | 0  0  0   1   4  4  1 0
.. .. ..    .. .o3.o3.x    ♦  0  4 |   0   0  6 |    0    0    0   4 |   *    *    *    *    * 560 ♦   0    0    0    0     0    0    4   6 |  0   0   0    0    0    0    0    6   12  12 |  0  0   0   0    0   0    0    0    4   6  12  4  4 | 0  0  0   0   1  4  4 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x.3o.3o. *b3o. .. .. ..    ♦  8  0 |  24   0  0 |   32    0    0   0 |   8    8    0    0    0   0 | 280    *    *    *     *    *    *   * |  3   0   3    0    0    0    0    0    0   0 |  3  0   6   3    0   0    0    0    0   0   0  0  0 | 1  3  3   1   0  0  0 0
x.3o. .. *b3o.3o. .. ..    ♦  5  0 |  10   0  0 |   10    0    0   0 |   0    5    0    0    0   0 |   * 1344    *    *     *    *    *   * |  1   2   0    2    0    0    0    0    0   0 |  2  1   2   0    0   2    1    0    0   0   0  0  0 | 1  2  1   0   0  1  0 0
xo3oo3oo    .. .. .. ..&#x ♦  4  1 |   6   4  0 |    4    6    0   0 |   1    0    4    0    0   0 |   *    * 2240    *     *    *    *   * |  0   0   3    0    3    0    0    0    0   0 |  0  0   3   6    3   0    0    0    0   0   0  0  0 | 0  1  3   3   3  1  0 0
xo3oo .. *b3oo .. .. ..&#x ♦  4  1 |   6   4  0 |    4    6    0   0 |   0    1    4    0    0   0 |   *    *    * 6720     *    *    *   * |  0   0   1    2    0    2    0    0    0   0 |  0  0   2   2    0   1    2    1    0   0   0  0  0 | 0  1  2   1   0  1  0 0
xo3oo ..    .. .. .. ox&#x ♦  3  2 |   3   6  1 |    1    6    3   0 |   0    0    2    3    0   0 |   *    *    *    * 13440    *    *   * |  0   0   0    0    1    2    2    0    0   0 |  0  0   0   2    2   0    1    2    1   0   0  0  0 | 0  0  1   2   1  1  0 0
xo .. ..    .. .. oo3ox&#x ♦  2  3 |   1   6  3 |    0    3    6   1 |   0    0    0    3    2   0 |   *    *    *    *     * 6720    *   * ♦  0   0   0    0    0    0    4    2    0   0 |  0  0   0   0    2   0    0    2    4   1   0  0  0 | 0  0  0   1   2  2  0 0
.. .. ..    .. oo3oo3ox&#x ♦  1  4 |   0   4  6 |    0    0    6   4 |   0    0    0    0    4   1 |   *    *    *    *     *    * 2240   * ♦  0   0   0    0    0    0    0    3    3   0 |  0  0   0   0    0   0    0    0    3   3   3  0  0 | 0  0  0   0   1  3  1 0
.. .. ..    .o3.o3.o3.x    ♦  0  5 |   0   0 10 |    0    0    0  10 |   0    0    0    0    0   5 |   *    *    *    *     *    *    * 672 ♦  0   0   0    0    0    0    0    0    2   4 |  0  0   0   0    0   0    0    0    0   1   4  2  2 | 0  0  0   0   0  2  2 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x.3o.3o. *b3o.3o. .. ..    ♦ 16  0 |  80   0  0 |  160    0    0   0 |  40   80    0    0    0   0 |  10   16    0    0     0    0    0   0 | 84   *   *    *    *    *    *    *    *   * |  2  0   2   0    0   0    0    0    0   0   0  0  0 | 1  2  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 |  * 448   *    *    *    *    *    *    *   * |  1  1   0   0    0   1    0    0    0   0   0  0  0 | 1  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 |  *   * 840    *    *    *    *    *    *   * |  0  0   2   2    0   0    0    0    0   0   0  0  0 | 0  1  2   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 |  *   *   * 2688    *    *    *    *    *   * |  0  0   1   0    0   1    1    0    0   0   0  0  0 | 0  1  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 |  *   *   *    * 3360    *    *    *    *   * |  0  0   0   2    2   0    0    0    0   0   0  0  0 | 0  0  1   2   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 |  *   *   *    *    * 6720    *    *    *   * |  0  0   0   1    0   0    1    1    0   0   0  0  0 | 0  0  1   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 |  *   *   *    *    *    * 8960    *    *   * |  0  0   0   0    1   0    0    1    1   0   0  0  0 | 0  0  0   1   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 |  *   *   *    *    *    *    * 3360    *   * |  0  0   0   0    0   0    0    0    2   1   0  0  0 | 0  0  0   0   1  2  0 0
.. .. ..    oo3oo3oo3ox&#x ♦  1  5 |   0   5 10 |    0    0   10  10 |   0    0    0    0   10   5 |   0    0    0    0     0    0    5   1 |  *   *   *    *    *    *    *    * 1344   * |  0  0   0   0    0   0    0    0    0   1   2  0  0 | 0  0  0   0   0  2  1 0
.. .o .. *b3.o3.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 |  *   *   *    *    *    *    *    *    * 448 |  0  0   0   0    0   0    0    0    0   0   1  1  1 | 0  0  0   0   0  1  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 | 14  *   *   *    *   *    *    *    *   *   *  *  * | 1  1  0   0   0  0  0 0
x.3o. .. *b3o.3o.3o.3o.    ♦  7  0 |  21   0  0 |   35    0    0   0 |   0   35    0    0    0   0 |   0   21    0    0     0    0    0   0 |  0   7   0    0    0    0    0    0    0   0 |  * 64   *   *    *   *    *    *    *   *   *  *  * | 1  0  0   0   0  1  0 0
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 |  *  * 168   *    *   *    *    *    *   *   *  *  * | 0  1  1   0   0  0  0 0
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 |  *  *   * 840    *   *    *    *    *   *   *  *  * | 0  0  1   1   0  0  0 0
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 |  *  *   *   * 2240   *    *    *    *   *   *  *  * | 0  0  0   1   1  0  0 0
xo3oo .. *b3oo3oo3oo ..&#x ♦  6  1 |  15   6  0 |   20   15    0   0 |   0   15   20    0    0   0 |   0    6    0   15     0    0    0   0 |  0   1   0    6    0    0    0    0    0   0 |  *  *   *   *    * 448    *    *    *   *   *  *  * | 0  1  0   0   0  1  0 0
xo3oo .. *b3oo3oo .. ox&#x ♦  5  2 |  10  10  1 |   10   20    5   0 |   0    5   20   10    0   0 |   0    1    0   10    10    0    0   0 |  0   0   0    2    0    5    0    0    0   0 |  *  *   *   *    *   * 1344    *    *   *   *  *  * | 0  0  1   0   0  1  0 0
xo3oo .. *b3oo .. oo3ox&#x ♦  4  3 |   6  12  3 |    4   18   12   1 |   0    1   12   18    4   0 |   0    0    0    3    12    6    0   0 |  0   0   0    0    0    3    4    0    0   0 |  *  *   *   *    *   *    * 2240    *   *   *  *  * | 0  0  0   1   0  1  0 0
xo3oo ..    .. oo3oo3ox&#x ♦  3  4 |   3  12  6 |    1   12   18   4 |   0    0    4   18   12   1 |   0    0    0    0     6   12    3   0 |  0   0   0    0    0    0    4    3    0   0 |  *  *   *   *    *   *    *    * 2240   *   *  *  * | 0  0  0   0   1  1  0 0
xo .. ..    oo3oo3oo3ox&#x ♦  2  5 |   1  10 10 |    0    5   20  10 |   0    0    0   10   20   5 |   0    0    0    0     0   10   10   1 |  0   0   0    0    0    0    0    5    2   0 |  *  *   *   *    *   *    *    *    * 672   *  *  * | 0  0  0   0   0  2  0 0
.. oo .. *b3oo3oo3oo3ox&#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   1 |  *  *   *   *    *   *    *    *    *   * 448  *  * | 0  0  0   0   0  1  1 0
.o3.o .. *b3.o3.o3.o3.x    ♦  0  7 |   0   0 21 |    0    0    0  35 |   0    0    0    0    0  35 |   0    0    0    0     0    0    0  21 |  0   0   0    0    0    0    0    0    0   7 |  *  *   *   *    *   *    *    *    *   *   * 64  * | 0  0  0   0   0  1  0 1
.. .o3.o *b3.o3.o3.o3.x    ♦  0  7 |   0   0 21 |    0    0    0  35 |   0    0    0    0    0  35 |   0    0    0    0     0    0    0  21 |  0   0   0    0    0    0    0    0    0   7 |  *  *   *   *    *   *    *    *    *   *   *  * 64 | 0  0  0   0   0  0  1 1
---------------------------+-------+------------+--------------------+-----------------------------+----------------------------------------+----------------------------------------------+-----------------------------------------------------+------------------------
x.3o.3o. *b3o.3o.3o.3o.    ♦ 64  0 | 672   0  0 | 2240    0    0   0 | 560 2240    0    0    0   0 | 280 1344    0    0     0    0    0   0 | 84 448   0    0    0    0    0    0    0   0 | 14 64   0   0    0   0    0    0    0   0   0  0  0 | 1  *  *   *   *  *  * *
xo3oo3oo *b3oo3oo3oo ..&#x ♦ 32  1 | 240  32  0 |  640  240    0   0 | 160  480  640    0    0   0 |  60  192  160  480     0    0    0   0 | 12  32  60  192    0    0    0    0    0   0 |  1  0  12   0    0  32    0    0    0   0   0  0  0 | * 14  *   *   *  *  * *
xo3oo3oo *b3oo3oo .. ox&#x ♦ 16  2 |  80  32  1 |  160  160   16   0 |  40   80  320   80    0   0 |  10   16   80  160   160    0    0   0 |  1   0  20   32   40   80    0    0    0   0 |  0  0   2  10    0   0   16    0    0   0   0  0  0 | *  * 84   *   *  *  * *
xo3oo3oo *b3oo .. oo3ox&#x ♦  8  3 |  24  24  3 |   32   72   24   1 |   8    8   96   72    8   0 |   1    0   24   24    96   24    0   0 |  0   0   3    0   24   24   32    0    0   0 |  0  0   0   3    8   0    0    8    0   0   0  0  0 | *  *  * 280   *  *  * *
xo3oo3oo    .. oo3oo3ox&#x ♦  4  4 |   6  16  6 |    4   24   24   4 |   1    0   16   36   16   1 |   0    0    4    0    24   24    4   0 |  0   0   0    0    6    0   16    6    0   0 |  0  0   0   0    4   0    0    0    4   0   0  0  0 | *  *  *   * 560  *  * *
xo3oo .. *b3oo3oo3oo3ox&#x ♦  7  7 |  21  42 21 |   35  105  105  35 |   0   35  140  210  140  35 |   0   21    0  105   210  210  105  21 |  0   7   0   42    0  105  140  105   42   7 |  0  1   0   0    0   7   21   35   35  21   7  1  0 | *  *  *   *   * 64  * *
.. oo3oo *b3oo3oo3oo3ox&#x ♦  1  7 |   0   7 21 |    0    0   21  35 |   0    0    0    0   35  35 |   0    0    0    0     0    0   35  21 |  0   0   0    0    0    0    0    0   21   7 |  0  0   0   0    0   0    0    0    0   0   7  0  1 | *  *  *   *   *  * 64 *
.o3.o3.o *b3.o3.o3.o3.x    ♦  0 14 |   0   0 84 |    0    0    0 280 |   0    0    0    0    0 560 |   0    0    0    0     0    0    0 672 |  0   0   0    0    0    0    0    0    0 448 |  0  0   0   0    0   0    0    0    0   0   0 64 64 | *  *  *   *   *  *  * 1
```

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