Acronym bragabrox
Name brag atop brox,
brag-first rotunda of sez
Circumradius sqrt(2) = 1.414214
Lace city
in approx. ASCII-art
r   N   r		- o3o3x3o3o4o (brag)
         
N   R   N		- o3o3o3x3o4o (brox)

where:
r - o3x3o3o4o (rat)
N - o3o3x3o4o (nit)
R - o3o3o3x4o (rin)
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0)   & all permutations, all changes of sign – but last coord. non-negative
Confer
uniform relative:
sez  
general polytopal classes:
segmentoexa   fundamental lace prisms  

Incidence matrix according to Dynkin symbol

oo3oo3xo3ox3oo4oo&#x   → height =  = 1/sqrt(2) = 0.707107
(brag || brox)

o.3o.3o.3o.3o.4o.    | 160   *    18   6    0 |  18   36   18   12    0    0 |   6  36  24  18   36    8   0   0   0 |  12  24  3   6  36  24   1   0   0  0 |  8  3  12  24  3  0  0 | 1  8  3 0
.o3.o3.o3.o3.o4.o    |   * 240 |    0   4   16 |   0    0    6   16   24   16 |   0   0   0   4   24   16  16  24   4 |   0   0  0   1  16  24   4   4  16  6 |  0  0   4  16  6  4  4 | 0  4  4 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
.. .. x. .. .. ..    |   2   0 | 1440   *    * |   2    4    1    0    0    0 |   1   8   4   2    4    0   0   0   0 |   4   8  1   1   8   4   0   0   0  0 |  4  2   4   8  1  0  0 | 1  4  2 0
oo3oo3oo3oo3oo4oo&#x |   1   1 |    * 960    * |   0    0    3    4    0    0 |   0   0   0   3   12    4   0   0   0 |   0   0  0   1  12  12   1   0   0  0 |  0  0   4  12  3  0  0 | 0  4  3 0
.. .. .. .x .. ..    |   0   2 |    *   * 1920 |   0    0    0    1    3    2 |   0   0   0   0    3    2   3   6   1 |   0   0  0   0   3   6   1   1   6  3 |  0  0   1   6  3  2  3 | 0  2  3 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
.. o.3x. .. .. ..    |   3   0 |    3   0    0 | 960    *    *    *    *    * |   1   4   0   1    0    0   0   0   0 |   4   4  0   1   4   0   0   0   0  0 |  4  1   4   4  0  0  0 | 1  4  1 0
.. .. x.3o. .. ..    |   3   0 |    3   0    0 |   * 1920    *    *    *    * |   0   2   2   0    1    0   0   0   0 |   1   4  1   0   2   2   0   0   0  0 |  2  2   1   4  1  0  0 | 1  2  2 0
.. .. xo .. .. ..&#x |   2   1 |    1   2    0 |   *    * 1440    *    *    * |   0   0   0   2    4    0   0   0   0 |   0   0  0   1   8   4   0   0   0  0 |  0  0   4   8  1  0  0 | 0  4  2 0
.. .. .. ox .. ..&#x |   1   2 |    0   2    1 |   *    *    * 1920    *    * |   0   0   0   0    3    2   0   0   0 |   0   0  0   0   3   6   1   0   0  0 |  0  0   1   6  3  0  0 | 0  2  3 0
.. .. .o3.x .. ..    |   0   3 |    0   0    3 |   *    *    *    * 1920    * |   0   0   0   0    1    0   2   2   0 |   0   0  0   0   2   2   0   1   4  1 |  0  0   1   4  1  2  2 | 0  2  2 1
.. .. .. .x3.o ..    |   0   3 |    0   0    3 |   *    *    *    *    * 1280 |   0   0   0   0    0    1   0   3   1 |   0   0  0   0   0   3   1   0   3  3 |  0  0   0   3  3  1  3 | 0  1  3 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
o.3o.3x. .. .. ..       4   0 |    6   0    0 |   4    0    0    0    0    0 | 240   *   *   *    *    *   *   *   * |   4   0  0   1   0   0   0   0   0  0 |  4  0   4   0  0  0  0 | 1  4  0 0
.. o.3x.3o. .. ..       6   0 |   12   0    0 |   4    4    0    0    0    0 |   * 960   *   *    *    *   *   *   * |   1   2  0   0   1   0   0   0   0  0 |  2  1   1   2  0  0  0 | 1  2  1 0
.. .. x.3o.3o. ..       4   0 |    6   0    0 |   0    4    0    0    0    0 |   *   * 960   *    *    *   *   *   * |   0   2  1   0   0   1   0   0   0  0 |  1  2   0   2  1  0  0 | 1  1  2 0
.. oo3xo .. .. ..&#x    3   1 |    3   3    0 |   1    0    3    0    0    0 |   *   *   * 960    *    *   *   *   * |   0   0  0   1   4   0   0   0   0  0 |  0  0   4   4  0  0  0 | 0  4  1 0
.. .. xo3ox .. ..&#x    3   3 |    3   6    3 |   0    1    3    3    1    0 |   *   *   *   * 1920    *   *   *   * |   0   0  0   0   2   2   0   0   0  0 |  0  0   1   4  1  0  0 | 0  2  2 0
.. .. .. ox3oo ..&#x    1   3 |    0   3    3 |   0    0    0    3    0    1 |   *   *   *   *    * 1280   *   *   * |   0   0  0   0   0   3   1   0   0  0 |  0  0   0   3  3  0  0 | 0  1  3 0
.. .o3.o3.x .. ..       0   4 |    0   0    6 |   0    0    0    0    4    0 |   *   *   *   *    *    * 960   *   * |   0   0  0   0   1   0   0   1   2  0 |  0  0   1   2  0  2  1 | 0  2  1 1
.. .. .o3.x3.o ..       0   6 |    0   0   12 |   0    0    0    0    4    4 |   *   *   *   *    *    *   * 960   * |   0   0  0   0   0   1   0   0   2  1 |  0  0   0   2  1  1  2 | 0  1  2 1
.. .. .. .x3.o4.o       0   6 |    0   0   12 |   0    0    0    0    0    8 |   *   *   *   *    *    *   *   * 160 |   0   0  0   0   0   0   1   0   0  3 |  0  0   0   0  3  0  3 | 0  0  3 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
o.3o.3x.3o. .. ..      10   0 |   30   0    0 |  20   10    0    0    0    0 |   5   5   0   0    0    0   0   0   0 | 192   *  *   *   *   *   *   *   *  * |  2  0   1   0  0  0  0 | 1  2  0 0
.. o.3x.3o.3o. ..      10   0 |   30   0    0 |  10   20    0    0    0    0 |   0   5   5   0    0    0   0   0   0 |   * 384  *   *   *   *   *   *   *  * |  1  1   0   1  0  0  0 | 1  1  1 0
.. .. x.3o.3o.4o.       8   0 |   24   0    0 |   0   32    0    0    0    0 |   0   0  16   0    0    0   0   0   0 |   *   * 60   *   *   *   *   *   *  * |  0  2   0   0  1  0  0 | 1  0  2 0
oo3oo3xo .. .. ..&#x    4   1 |    6   4    0 |   4    0    6    0    0    0 |   1   0   0   4    0    0   0   0   0 |   *   *  * 240   *   *   *   *   *  * |  0  0   4   0  0  0  0 | 0  4  0 0
.. oo3xo3ox .. ..&#x    6   4 |   12  12    6 |   4    4   12    6    4    0 |   0   1   0   4    4    0   1   0   0 |   *   *  *   * 960   *   *   *   *  * |  0  0   1   2  0  0  0 | 0  2  1 0
.. .. xo3ox3oo ..&#x    4   6 |    6  12   12 |   0    4    6   12    4    4 |   0   0   1   0    4    4   0   1   0 |   *   *  *   *   * 960   *   *   *  * |  0  0   0   2  1  0  0 | 0  1  2 0
.. .. .. ox3oo4oo&#x    1   6 |    0   6   12 |   0    0    0   12    0    8 |   0   0   0   0    0    8   0   0   1 |   *   *  *   *   *   * 160   *   *  * |  0  0   0   0  3  0  0 | 0  0  3 0
.o3.o3.o3.x .. ..       0   5 |    0   0   10 |   0    0    0    0   10    0 |   0   0   0   0    0    0   5   0   0 |   *   *  *   *   *   *   * 192   *  * |  0  0   1   0  0  2  0 | 0  2  0 1
.. .o3.o3.x3.o ..       0  10 |    0   0   30 |   0    0    0    0   20   10 |   0   0   0   0    0    0   5   5   0 |   *   *  *   *   *   *   *   * 384  * |  0  0   0   1  0  1  1 | 0  1  1 1
.. .. .o3.x3.o4.o       0  24 |    0   0   96 |   0    0    0    0   32   64 |   0   0   0   0    0    0   0  16   8 |   *   *  *   *   *   *   *   *   * 60 |  0  0   0   0  1  0  2 | 0  0  2 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
o.3o.3x.3o.3o. ..      20   0 |   90   0    0 |  60   60    0    0    0    0 |  15  30  15   0    0    0   0   0   0 |   6   6  0   0   0   0   0   0   0  0 | 64  *   *   *  *  *  * | 1  1  0 0
.. o.3x.3o.3o.4o.      40   0 |  240   0    0 |  80  320    0    0    0    0 |   0  80 160   0    0    0   0   0   0 |   0  32 10   0   0   0   0   0   0  0 |  * 12   *   *  *  *  * | 1  0  1 0
oo3oo3xo3ox .. ..&#x   10   5 |   30  20   10 |  20   10   30   10   10    0 |   5   5   0  20   10    0   5   0   0 |   1   0  0   5   5   0   0   1   0  0 |  *  * 192   *  *  *  * | 0  2  0 0
.. oo3xo3ox3oo ..&#x   10  10 |   30  30   30 |  10   20   30   30   20   10 |   0   5   5  10   20   10   5   5   0 |   0   1  0   0   5   5   0   0   1  0 |  *  *   * 384  *  *  * | 0  1  1 0
.. .. xo3ox3oo4oo&#x    8  24 |   24  48   96 |   0   32   24   96   32   64 |   0   0  16   0   32   64   0  16   8 |   0   0  1   0   0  16   8   0   0  1 |  *  *   *   * 60  *  * | 0  0  2 0
.o3.o3.o3.x3.o ..       0  15 |    0   0   60 |   0    0    0    0   60   20 |   0   0   0   0    0    0  30  15   0 |   0   0  0   0   0   0   0   6   6  0 |  *  *   *   *  * 64  * | 0  1  0 1
.. .o3.o3.x3.o4.o       0  80 |    0   0  480 |   0    0    0    0  320  320 |   0   0   0   0    0    0  80 160  40 |   0   0  0   0   0   0   0   0  32 10 |  *  *   *   *  *  * 12 | 0  0  1 1
---------------------+---------+---------------+------------------------------+---------------------------------------+---------------------------------------+------------------------+----------
o.3o.3x.3o.3o.4o.     160   0 | 1440   0    0 | 960 1920    0    0    0    0 | 240 960 960   0    0    0   0   0   0 | 192 384 60   0   0   0   0   0   0  0 | 64 12   0   0  0  0  0 | 1  *  * *
oo3oo3xo3ox3oo ..&#x   20  15 |   90  60   60 |  60   60   90   60   60   20 |  15  30  15  60   60   20  30  15   0 |   6   6  0  15  30  15   0   6   6  0 |  1  0   6   6  0  1  0 | * 64  * *
.. oo3xo3ox3oo4oo&#x   40  80 |  240 240  480 |  80  320  240  480  320  320 |   0  80 160  80  320  320  80 160  40 |   0  32 10   0  80 160  40   0  32 10 |  0  1   0  32 10  0  1 | *  * 12 *
.o3.o3.o3.x3.o4.o       0 240 |    0   0 1920 |   0    0    0    0 1920 1280 |   0   0   0   0    0    0 960 960 160 |   0   0  0   0   0   0   0 192 384 60 |  0  0   0   0  0 64 12 | *  *  * 1

oo3xo3oo *b3ox3oo3oo&#x   → height =  = 1/sqrt(2) = 0.707107
(brag || brox)

...

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