Acronym zarez
Name zee atop rez,
rectified diacosipentacontahexazetton half
Circumradius 1
Lace city
in approx. ASCII-art 
o   g   o	-- x3o3o3o3o3o4o (zee)
         
g   r   g	-- o3x3o3o3o3o4o (rez)

where:
o = o3o3o3o3o4o (point)
g = x3o3o3o3o4o (gee)
r = o3x3o3o3o4o (rag)

  h   H  	-- x3o3o3o3o3o4o (zee)
         
         
r   S   R	-- o3x3o3o3o3o4o (rez)

where:
h = x3o3o3o3o3o (hop)
H = o3o3o3o3o3x (dual hop)
r = o3x3o3o3o3o (ril)
R = o3o3o3o3x3o (inv. ril)
S = x3o3o3o3o3x (staf)
Coordinates
  1. (1/sqrt(2), 0, 0, 0, 0, 0, 0; 1/sqrt(2))   & permutations and changes of sign in all but last coord.
    (zee layer)
  2. (1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0, 0; 0)   & permutations and changes of sign in all but last coord.
    (rez layer)
Volume 31/630 = 0.049206
Dihedral angles
  • at ril between roc and roc:   arccos(-3/4) = 138.590378°
  • at hop between roc and zee:   arccos[-1/sqrt(8)] = 110.704811°
  • at gee between geepy and rez:   90°
  • at ril between rez and roc:   arccos[1/sqrt(8)] = 69.295189°
Face vector 98, 1092, 3724, 7000, 7952, 5152, 1614, 144
Confer
uniform relative:
rek  
general polytopal classes:
segmentozetta   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

xo3ox3oo3oo3oo3oo4oo&#x   → height = 1/sqrt(2) = 0.707107
(zee || rez)

o.3o.3o.3o.3o.3o.4o.    | 14  * ♦ 12  12   0 |  60 12  60   0    0 | 160  60  160   0    0 | 240 160  240   0    0 | 192 240  192   0   0 |  64 192  64   0  0 | 1  64  1 0
.o3.o3.o3.o3.o3.o4.o    |  * 84 |  0   2  20 |   0  1  20  10   80 |   0  10   80  40  160 |   0  40  160  80  160 |   0  80  160  80  64 |   0  80  64  32  1 | 0  32  2 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x. .. .. .. .. .. ..    |  2  0 | 84   *   * |  10  1   0   0    0 |  40  10    0   0    0 |  80  40    0   0    0 |  80  80    0   0   0 |  32  80   0   0  0 | 1  32  0 0
oo3oo3oo3oo3oo3oo4oo&#x |  1  1 |  * 168   * |   0  1  10   0    0 |   0  10   40   0    0 |   0  40   80   0    0 |   0  80   80   0   0 |   0  80  30   0  0 | 0  32  1 0
.. .x .. .. .. .. ..    |  0  2 |  *   * 840 |   0  0   1   1    8 |   0   1    8   8   24 |   0   8   24  24   32 |   0  24   32  32  16 |   0  32  16  16  1 | 0  16  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o. .. .. .. .. ..    |  3  0 |  3   0   0 | 280  *   *   *    * |   8   1    0   0    0 |  24   8    0   0    0 |  32  24    0   0   0 |  16  32   0   0  0 | 1  16  0 0
xo .. .. .. .. .. ..&#x |  2  1 |  1   2   0 |   * 84   *   *    * ♦   0  10    0   0    0 |   0  40    0   0    0 |   0  80    0   0   0 |   0  80   0   0  0 | 0  32  0 0
.. ox .. .. .. .. ..&#x |  1  2 |  0   2   1 |   *  * 840   *    * |   0   1    8   0    0 |   0   8   24   0    0 |   0  24   32   0   0 |   0  32  16   0  0 | 0  16  1 0
.o3.x .. .. .. .. ..    |  0  3 |  0   0   3 |   *  *   * 280    * ♦   0   1    0   8    0 |   0   8    0  24    0 |   0  24    0  32   0 |   0  32   0  16  0 | 0  16  0 1
.. .x3.o .. .. .. ..    |  0  3 |  0   0   3 |   *  *   *   * 2240 |   0   0    1   1    6 |   0   1    6   6   12 |   0   6   12  12   8 |   0  12   8   8  1 | 0   8  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o.3o. .. .. .. ..    ♦  4  0 |  6   0   0 |   4  0   0   0    0 | 560   *    *   *    * |   6   1    0   0    0 |  12   6    0   0   0 |   8  12   0   0  0 | 1   8  0 0
xo3ox .. .. .. .. ..&#x ♦  3  3 |  3   6   3 |   1  3   3   1    0 |   * 280    *   *    * ♦   0   8    0   0    0 |   0  24    0   0   0 |   0  32   0   0  0 | 0  16  0 0
.. ox3oo .. .. .. ..&#x ♦  1  3 |  0   3   3 |   0  0   3   0    1 |   *   * 2240   *    * |   0   1    6   0    0 |   0   6   12   0   0 |   0  12   8   0  0 | 0   8  1 0
.o3.x3.o .. .. .. ..    ♦  0  6 |  0   0  12 |   0  0   0   4    4 |   *   *    * 560    * ♦   0   1    0   6    0 |   0   6    0  12   0 |   0  12   0   8  0 | 0   8  0 1
.. .x3.o3.o .. .. ..    ♦  0  4 |  0   0   6 |   0  0   0   0    4 |   *   *    *   * 3360 |   0   0    1   1    4 |   0   1    4   4   4 |   0   4   4   4  1 | 0   4  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o.3o.3o. .. .. ..    ♦  5  0 | 10   0   0 |  10  0   0   0    0 |   5   0    0   0    0 | 672   *    *   *    * |   4   1    0   0   0 |   4   4   0   0  0 | 1   4  0 0
xo3ox3oo .. .. .. ..&#x ♦  4  6 |  6  12  12 |   4  6  12   4    4 |   1   4    4   1    0 |   * 560    *   *    * ♦   0   6    0   0   0 |   0  12   0   0  0 | 0   8  0 0
.. ox3oo3oo .. .. ..&#x ♦  1  4 |  0   4   6 |   0  0   6   0    4 |   0   0    4   0    1 |   *   * 3360   *    * |   0   1    4   0   0 |   0   4   4   0  0 | 0   4  1 0
.o3.x3.o3.o .. .. ..    ♦  0 10 |  0   0  30 |   0  0   0  10   20 |   0   0    0   5    5 |   *   *    * 672    * ♦   0   1    0   4   0 |   0   4   0   4  0 | 0   4  0 1
.. .x3.o3.o3.o .. ..    ♦  0  5 |  0   0  10 |   0  0   0   0   10 |   0   0    0   0    5 |   *   *    *   * 2688 |   0   0    1   1   2 |   0   1   2   2  1 | 0   2  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o.3o.3o.3o. .. ..    ♦  6  0 | 15   0   0 |  20  0   0   0    0 |  15   0    0   0    0 |   6   0    0   0    0 | 448   *    *   *   * |   2   1   0   0  0 | 1   2  0 0
xo3ox3oo3oo .. .. ..&#x ♦  5 10 | 10  20  30 |  10 10  30  10   20 |   5  10   20   5    5 |   1   5    5   1    0 |   * 672    *   *   * |   0   4   0   0  0 | 0   4  0 0
.. ox3oo3oo3oo .. ..&#x ♦  1  5 |  0   5  10 |   0  0  10   0   10 |   0   0   10   0    5 |   0   0    5   0    1 |   *   * 2688   *   * |   0   1   2   0  0 | 0   2  1 0
.o3.x3.o3.o3.o .. ..    ♦  0 15 |  0   0  60 |   0  0   0  20   60 |   0   0    0  15   30 |   0   0    0   6    6 |   *   *    * 448   * |   0   1   0   2  0 | 0   2  0 1
.. .x3.o3.o3.o3.o ..    ♦  0  6 |  0   0  15 |   0  0   0   0   20 |   0   0    0   0   15 |   0   0    0   0    6 |   *   *    *   * 896 |   0   0   1   1  1 | 0   1  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o.3o.3o.3o.3o. ..    ♦  7  0 | 21   0   0 |  35  0   0   0    0 |  35   0    0   0    0 |  21   0    0   0    0 |   7   0    0   0   0 | 128   *   *   *  * | 1   1  0 0
xo3ox3oo3oo3oo .. ..&#x ♦  6 15 | 15  30  60 |  20 15  60  20   60 |  15  20   60  15   30 |   6  15   30   6    6 |   1   6    6   1   0 |   * 448   *   *  * | 0   2  0 0
.. ox3oo3oo3oo3oo ..&#x ♦  1  6 |  0   6  15 |   0  0  15   0   20 |   0   0   20   0   15 |   0   0   15   0    6 |   0   0    6   0   1 |   *   * 896   *  * | 0   1  1 0
.o3.x3.o3.o3.o3.o ..    ♦  0 21 |  0   0 105 |   0  0   0  35  140 |   0   0    0  35  105 |   0   0    0  21   42 |   0   0    0   7   7 |   *   *   * 128  * | 0   1  0 1
.. .x3.o3.o3.o3.o4.o    ♦  0 12 |  0   0  60 |   0  0   0   0  160 |   0   0    0   0  240 |   0   0    0   0  192 |   0   0    0   0  64 |   *   *   *   * 14 | 0   0  1 1
------------------------+-------+------------+---------------------+-----------------------+-----------------------+----------------------+--------------------+-----------
x.3o.3o.3o.3o.3o.4o.    ♦ 14  0 | 84   0   0 | 280  0   0   0    0 | 560   0    0   0    0 | 672   0    0   0    0 | 448   0    0   0   0 | 128   0   0   0  0 | 1   *  * *
xo3ox3oo3oo3oo3oo ..&#x ♦  7 21 | 21  42 105 |  35 21 105  35  140 |  35  35  140  35  105 |  21  35  105  21   42 |   7  21   42   7   7 |   1   7   7   1  0 | * 128  * *
.. ox3oo3oo3oo3oo4oo&#x ♦  1 12 |  0  12  60 |   0  0  60   0  160 |   0   0  160   0  240 |   0   0  240   0  192 |   0   0  192   0  64 |   0   0  64   0  1 | *   * 14 *
.o3.x3.o3.o3.o3.o4.o    ♦  0 84 |  0   0 840 |   0  0   0 280 2240 |   0   0    0 560 3360 |   0   0    0 672 2688 |   0   0    0 448 896 |   0   0   0 128 14 | *   *  * 1


oo3oo3oo *b3oo3oo3xo3ox&#x   → height = 1/sqrt(2) = 0.707107
(zee || rez)

o.3o.3o. *b3o.3o.3o.3o.    | 14  * ♦ 12  12   0 |  60  60 12    0   0 | 160  160  60    0   0 | 240  240 160    0   0 | 192  192 240   0   0   0 | 32 32  32  32 192  0  0  0 | 1  1 32 32 0
.o3.o3.o *b3.o3.o3.o3.o    |  * 84 |  0   2  20 |   0  20  1   80  10 |   0   80  10  160  40 |   0  160  40  160  80 |   0  160  80  32  32  80 |  0  0  32  32  80  2 16 16 | 0  2 16 16 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
.. .. ..    .. .. .. x.    |  2  0 | 84   *   * |  10   0  1    0   0 |  40    0  10    0   0 |  80    0  40    0   0 |  80    0  80   0   0   0 | 16 16   0   0  80  0  0  0 | 1  0 16 16 0
oo3oo3oo *b3oo3oo3oo3oo&#x |  1  1 |  * 168   * |   0  10  1    0   0 |   0   40  10    0   0 |   0   80  40    0   0 |   0   80  80   0   0   0 |  0  0  16  16  80  0  0  0 | 0  1 16 16 0
.. .. ..    .. .. .x ..    |  0  2 |  *   * 840 |   0   1  0    8   1 |   0    8   1   24   8 |   0   24   8   32  24 |   0   32  24   8   8  32 |  0  0   8   8  32  1  8  8 | 0  1  8  8 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
.. .. ..    .. .. o.3x.    |  3  0 |  3   0   0 | 280   *  *    *   * |   8    0   1    0   0 |  24    0   8    0   0 |  32    0  24   0   0   0 |  8  8   0   0  32  0  0  0 | 1  0  8  8 0
.. .. ..    .. .. ox ..&#x |  1  2 |  0   2   1 |   * 840  *    *   * |   0    8   1    0   0 |   0   24   8    0   0 |   0   32  24   0   0   0 |  0  0   8   8  32  0  0  0 | 0  1  8  8 0
.. .. ..    .. .. .. xo&#x |  2  1 |  1   2   0 |   *   * 84    *   * ♦   0    0  10    0   0 |   0    0  40    0   0 |   0    0  80   0   0   0 |  0  0   0   0  80  0  0  0 | 0  0 16 16 0
.. .. ..    .. .o3.x ..    |  0  3 |  0   0   3 |   *   *  * 2240   * |   0    1   0    6   1 |   0    6   1   12   6 |   0   12   6   4   4  12 |  0  0   4   4  12  1  4  4 | 0  1  4  4 1
.. .. ..    .. .. .x3.o    |  0  3 |  0   0   3 |   *   *  *    * 280 ♦   0    0   1    0   8 |   0    0   8    0  24 |   0    0  24   0   0  32 |  0  0   0   0  32  0  8  8 | 0  0  8  8 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
.. .. ..    .. o.3o.3x.    ♦  4  0 |  6   0   0 |   4   0  0    0   0 | 560    *   *    *   * |   6    0   1    0   0 |  12    0   6   0   0   0 |  4  4   0   0  12  0  0  0 | 1  0  4  4 0
.. .. ..    .. oo3ox ..&#x ♦  1  3 |  0   3   3 |   0   3  0    1   0 |   * 2240   *    *   * |   0    6   1    0   0 |   0   12   6   0   0   0 |  0  0   4   4  12  0  0  0 | 0  1  4  4 0
.. .. ..    .. .. ox3xo&#x ♦  3  3 |  3   6   3 |   1   3  3    0   1 |   *    * 280    *   * ♦   0    0   8    0   0 |   0    0  24   0   0   0 |  0  0   0   0  32  0  0  0 | 0  0  8  8 0
.. .. ..    .o3.o3.x ..    ♦  0  4 |  0   0   6 |   0   0  0    4   0 |   *    *   * 3360   * |   0    1   0    4   1 |   0    4   1   2   2   4 |  0  0   2   2   4  1  2  2 | 0  1  2  2 1
.. .. ..    .. .o3.x3.o    ♦  0  6 |  0   0  12 |   0   0  0    4   4 |   *    *   *    * 560 ♦   0    0   1    0   6 |   0    0   6   0   0  12 |  0  0   0   0  12  0  4  4 | 0  0  4  4 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
.. .. ..    o.3o.3o.3x.    ♦  5  0 | 10   0   0 |  10   0  0    0   0 |   5    0   0    0   0 | 672    *   *    *   * |   4    0   1   0   0   0 |  2  2   0   0   4  0  0  0 | 1  0  2  2 0
.. .. ..    oo3oo3ox ..&#x ♦  1  4 |  0   4   6 |   0   6  0    4   0 |   0    4   0    1   0 |   * 3360   *    *   * |   0    4   1   0   0   0 |  0  0   2   2   4  0  0  0 | 0  1  2  2 0
.. .. ..    .. oo3ox3xo&#x ♦  4  6 |  6  12  12 |   4  12  6    4   4 |   1    4   4    0   1 |   *    * 560    *   * ♦   0    0   6   0   0   0 |  0  0   0   0  12  0  0  0 | 0  0  4  4 0
.. .o .. *b3.o3.o3.x ..    ♦  0  5 |  0   0  10 |   0   0  0   10   0 |   0    0   0    5   0 |   *    *   * 2688   * |   0    1   0   1   1   1 |  0  0   1   1   1  1  1  1 | 0  1  1  1 1
.. .. ..    .o3.o3.x3.o    ♦  0 10 |  0   0  30 |   0   0  0   20  10 |   0    0   0    5   5 |   *    *   *    * 672 ♦   0    0   1   0   0   4 |  0  0   0   0   4  0  2  2 | 0  0  2  2 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
.. o. .. *b3o.3o.3o.3x.    ♦  6  0 | 15   0   0 |  20   0  0    0   0 |  15    0   0    0   0 |   6    0   0    0   0 | 448    *   *   *   *   * |  1  1   0   0   1  0  0  0 | 1  0  1  1 0
.. oo .. *b3oo3oo3ox ..&#x ♦  1  5 |  0   5  10 |   0  10  0   10   0 |   0   10   0    5   0 |   0    5   0    1   0 |   * 2688   *   *   *   * |  0  0   1   1   1  0  0  0 | 0  1  1  1 0
.. .. ..    oo3oo3ox3xo&#x ♦  5 10 | 10  20  30 |  10  30 10   20  10 |   5   20  10    5   5 |   1    5   5    0   1 |   *    * 672   *   *   * |  0  0   0   0   4  0  0  0 | 0  0  2  2 0
.o3.o .. *b3.o3.o3.x ..    ♦  0  6 |  0   0  15 |   0   0  0   20   0 |   0    0   0   15   0 |   0    0   0    6   0 |   *    *   * 448   *   * |  0  0   1   0   0  1  1  0 | 0  1  1  0 1
.. .o3.o *b3.o3.o3.x ..    ♦  0  6 |  0   0  15 |   0   0  0   20   0 |   0    0   0   15   0 |   0    0   0    6   0 |   *    *   *   * 448   * |  0  0   0   1   0  1  0  1 | 0  1  0  1 1
.. .o .. *b3.o3.o3.x3.o    ♦  0 15 |  0   0  60 |   0   0  0   60  20 |   0    0   0   30  15 |   0    0   0    6   6 |   *    *   *   *   * 448 |  0  0   0   0   1  0  1  1 | 0  0  1  1 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
o.3o. .. *b3o.3o.3o.3x.    ♦  7  0 | 21   0   0 |  35   0  0    0   0 |  35    0   0    0   0 |  21    0   0    0   0 |   7    0   0   0   0   0 | 64  *   *   *   *  *  *  * | 1  0  1  0 0
.. o.3o. *b3o.3o.3o.3x.    ♦  7  0 | 21   0   0 |  35   0  0    0   0 |  35    0   0    0   0 |  21    0   0    0   0 |   7    0   0   0   0   0 |  * 64   *   *   *  *  *  * | 1  0  0  1 0
oo3oo .. *b3oo3oo3ox ..&#x ♦  1  6 |  0   6  15 |   0  15  0   20   0 |   0   20   0   15   0 |   0   15   0    6   0 |   0    6   0   1   0   0 |  *  * 448   *   *  *  *  * | 0  1  1  0 0
.. oo3oo *b3oo3oo3ox ..&#x ♦  1  6 |  0   6  15 |   0  15  0   20   0 |   0   20   0   15   0 |   0   15   0    6   0 |   0    6   0   0   1   0 |  *  *   * 448   *  *  *  * | 0  1  0  1 0
.. oo .. *b3oo3oo3ox3xo&#x ♦  6 15 | 15  30  60 |  20  60 15   60  20 |  15   60  20   30  15 |   6   30  15    6   6 |   1    6   6   0   0   1 |  *  *   *   * 448  *  *  * | 0  0  1  1 0
.o3.o3.o *b3.o3.o3.x ..    ♦  0 12 |  0   0  60 |   0   0  0  160   0 |   0    0   0  240   0 |   0    0   0  192   0 |   0    0   0  32  32   0 |  *  *   *   *   * 14  *  * | 0  1  0  0 1
.o3.o .. *b3.o3.o3.x3.o    ♦  0 21 |  0   0 105 |   0   0  0  140  35 |   0    0   0  105  35 |   0    0   0   42  21 |   0    0   0   7   0   7 |  *  *   *   *   *  * 64  * | 0  0  1  0 1
.. .o3.o *b3.o3.o3.x3.o    ♦  0 21 |  0   0 105 |   0   0  0  140  35 |   0    0   0  105  35 |   0    0   0   42  21 |   0    0   0   0   7   7 |  *  *   *   *   *  *  * 64 | 0  0  0  1 1
---------------------------+-------+------------+---------------------+-----------------------+-----------------------+--------------------------+----------------------------+-------------
o.3o.3o. *b3o.3o.3o.3x.    ♦ 14  0 | 84   0   0 | 280   0  0    0   0 | 560    0   0    0   0 | 672    0   0    0   0 | 448    0   0   0   0   0 | 64 64   0   0   0  0  0  0 | 1  *  *  * *
oo3oo3oo *b3oo3oo3ox ..&#x ♦  1 12 |  0  12  60 |   0  60  0  160   0 |   0  160   0  240   0 |   0  240   0  192   0 |   0  192   0  32  32   0 |  0  0  32  32   0  1  0  0 | * 14  *  * *
oo3oo .. *b3oo3oo3ox3xo&#x ♦  7 21 | 21  42 105 |  35 105 21  140  35 |  35  140  35  105  35 |  21  105  35   42  21 |   7   42  21   7   0   7 |  1  0   7   0   7  0  1  0 | *  * 64  * *
.. oo3oo *b3oo3oo3ox3xo&#x ♦  7 21 | 21  42 105 |  35 105 21  140  35 |  35  140  35  105  35 |  21  105  35   42  21 |   7   42  21   0   7   7 |  0  1   0   7   7  0  0  1 | *  *  * 64 *
.o3.o3.o *b3.o3.o3.x3.o    ♦  0 84 |  0   0 840 |   0   0  0 2240 280 |   0    0   0 3360 560 |   0    0   0 2688 672 |   0    0   0 448 448 448 |  0  0   0   0   0 14 64 64 | *  *  *  * 1

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