Acronym jakaljak
Name jak atop inverted jak,
medial segment of naq
Circumradius sqrt(3)/2 = 0.866025
Lace city
in approx. ASCII-art
          +---- hax
         /   +- tacpy
        /   /

  T   N   o  -- jak
           
o   n   T    -- inverted jak

          \
           +--- dijak
where:
o = o3o3o *b3o3o  (pt)
T = o3o3o *b3o3x  (tac)
N = x3o3o *b3o3o  (hin)
n = o3o3x *b3o3o  (alternate hin)
Confer
general polytopal classes:
segmentoexa   fundamental lace prisms   scaliform  

Incidence matrix according to Dynkin symbol

xo3oo3oo3oo3ox *c3oo&#x   → height = 1/sqrt(3) = 0.577350
(jak || inv jak)

o.3o.3o.3o.3o. *c3o.    & | 54 |  16  10 |   80  120 |  160  320  160 |  80  40  400  400 |  16 10  96  240  96  80 | 1 16 11  56
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x. .. .. .. ..    ..    & |  2 | 432   * |   10    5 |   30   30   10 |  20  10   60   40 |   5  5  20   35  20  10 | 1  5  5  11
oo3oo3oo3oo3oo *c3oo&#x   |  2 |   * 270 |    0   16 |    0   48   32 |   0   0   64   96 |   0  0  16   64  16  24 | 0  8  2  16
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x.3o. .. .. ..    ..    & |  3 |   3   0 | 1440    * |    6    3    0 |   6   3   12    3 |   2  3   6    6   6   1 | 1  2  3   3
xo .. .. .. ..    ..&#x & |  3 |   1   2 |    * 2160 |    0    6    4 |   0   0   12   18 |   0  0   4   16   4   6 | 0  4  1   5
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x.3o.3o. .. ..    ..    &   4 |   6   0 |    4    0 | 2160    *    * |   2   1    2    0 |   1  2   2    1   2   0 | 1  1  2   1
xo3oo .. .. ..    ..&#x &   4 |   3   3 |    1    3 |    * 4320    * |   0   0    4    2 |   0  0   2    4   2   1 | 0  2  1   2
xo .. .. .. ox    ..&#x     4 |   2   4 |    0    4 |    *    * 2160 |   0   0    0    6 |   0  0   0    6   0   3 | 0  3  0   2
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x.3o.3o.3o. ..    ..    &   5 |  10   0 |   10    0 |    5    0    0 | 864   *    *    * |   1  1   1    0   0   0 | 1  1  1   0
x.3o.3o. .. .. *c3o.    &   5 |  10   0 |   10    0 |    5    0    0 |   * 432    *    * |   0  2   0    0   2   0 | 1  0  2   1
xo3oo3oo .. ..    ..&#x &   5 |   6   4 |    4    6 |    1    4    0 |   *   * 4320    * |   0  0   1    1   1   0 | 0  1  1   1
xo3oo .. .. ox    ..&#x &   5 |   4   6 |    1    9 |    0    2    3 |   *   *    * 4320 |   0  0   0    2   0   1 | 0  2  0   1
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x.3o.3o.3o.3o.    ..    &   6 |  15   0 |   20    0 |   15    0    0 |   6   0    0    0 | 144  *   *    *   *   * | 1  1  0   0
x.3o.3o.3o. .. *c3o.    &  10 |  40   0 |   80    0 |   80    0    0 |  16  16    0    0 |   * 54   *    *   *   * | 1  0  1   0
xo3oo3oo3oo ..    ..&#x &   6 |  10   5 |   10   10 |    5   10    0 |   1   0    5    0 |   *  * 864    *   *   * | 0  1  1   0
xo3oo3oo .. ox    ..&#x &   6 |   7   8 |    4   16 |    1    8    6 |   0   0    2    4 |   *  *   * 2160   *   * | 0  1  0   1
xo3oo3oo .. .. *c3oo&#x &   6 |  10   5 |   10   10 |    5   10    0 |   0   1    5    0 |   *  *   *    * 864   * | 0  0  1   1
xo3oo .. oo3ox    ..&#x     6 |   6   9 |    2   18 |    0    6    9 |   0   0    0    6 |   *  *   *    *   * 720 | 0  2  0   0
--------------------------+----+---------+-----------+----------------+-------------------+-------------------------+------------
x.3o.3o.3o.3o. *c3o.    &  27 | 216   0 |  720    0 | 1080    0    0 | 432 216    0    0 |  72 27   0    0   0   0 | 2  *  *   *
xo3oo3oo3oo3ox    ..&#x    12 |  30  30 |   40  120 |   30  120   90 |  12   0   60  120 |   2  0  12   30   0  20 | * 72  *   *
xo3oo3oo3oo .. *c3oo&#x &  11 |  40  10 |   80   40 |   80   80    0 |  16  16   80    0 |   0  1  16    0  16   0 | *  * 54   *
xo3oo3oo .. ox *c3oo&#x &   7 |  11  10 |   10   25 |    5   20   10 |   0   1   10   10 |   0  0   0    5   2   0 | *  *  * 432

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