Acronym jakarojak
Name jak atop rojak,
jak-first cap of ranq
Circumradius sqrt(2) = 1.414214
Lace city
in approx. ASCII-art
  h R h  		-- x3o3o3o3o *c3o (jak)
r p X p r		-- o3x3o3o3o *c3o (rojak)

where:
h = x3o3o3o3o (hix)
r = o3x3o3o3o (rix)
R = o3o3o3x3o (inv. rix)
p = x3o3o3x3o (spix)
X = uo3oo3ox3oo3ox&#zx (tegum sum  of inv sarx and u-hix)
Face vector 243, 2808, 8136, 10440, 6318, 1575, 128
Confer
uniform relative:
ranq  
general polytopal classes:
segmentoexa   fundamental lace prisms   lace simplices  

Incidence matrix according to Dynkin symbol

xo3ox3oo3oo3oo *c3oo&#x   → height = 1/sqrt(3) = 0.577350
(jak || rojak)

o.3o.3o.3o.3o. *c3o.    | 27   *   16  16    0 |  80  16   80   0    0 |  160  80  160    0    0    0 |  80  40  160   80   40   0   0   0   0 | 16 10  80  40  16  10  0  0  0 | 1 16 10  1 0
.o3.o3.o3.o3.o *c3.o    |  * 216 |   0   2   20 |   0   1   20  10   60 |    0  10   60   30   40   20 |   0   0   30   40   20  20  10  10  10 |  0  0  20  10  10  10  5  5  2 | 0  5  5  2 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x. .. .. .. ..    ..    |  2   0 | 216   *    * |  10   1    0   0    0 |   30  10    0    0    0    0 |  20  10   30    0    0   0   0   0   0 |  5  5  20  10   0   0  0  0  0 | 1  5  5  0 0
oo3oo3oo3oo3oo *c3oo&#x |  1   1 |   * 432    * |   0   1   10   0    0 |    0  10   30    0    0    0 |   0   0   30   20   10   0   0   0   0 |  0  0  20  10   5   5  0  0  0 | 0  5  5  1 0
.. .x .. .. ..    ..    |  0   2 |   *   * 2160 |   0   0    1   1    6 |    0   1    6    6    6    3 |   0   0    6    6    3   6   3   2   3 |  0  0   6   3   2   3  2  3  1 | 0  2  3  1 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x.3o. .. .. ..    ..    |  3   0 |   3   0    0 | 720   *    *   *    * |    6   1    0    0    0    0 |   6   3    6    0    0   0   0   0   0 |  2  3   6   3   0   0  0  0  0 | 1  2  3  0 0
xo .. .. .. ..    ..&#x |  2   1 |   1   2    0 |   * 216    *   *    *     0  10    0    0    0    0 |   0   0   30    0    0   0   0   0   0 |  0  0  20  10   0   0  0  0  0 | 0  5  5  0 0
.. ox .. .. ..    ..&#x |  1   2 |   0   2    1 |   *   * 2160   *    * |    0   1    6    0    0    0 |   0   0    6    6    3   0   0   0   0 |  0  0   6   3   2   3  0  0  0 | 0  2  3  1 0
.o3.x .. .. ..    ..    |  0   3 |   0   0    3 |   *   *    * 720    * |    0   1    0    6    0    0 |   0   0    6    0    0   6   3   0   0 |  0  0   6   3   0   0  2  3  0 | 0  2  3  0 1
.. .x3.o .. ..    ..    |  0   3 |   0   0    3 |   *   *    *   * 4320 |    0   0    1    1    2    1 |   0   0    1    2    1   2   1   1   2 |  0  0   2   1   1   2  1  2  1 | 0  1  2  1 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x.3o.3o. .. ..    ..      4   0 |   6   0    0 |   4   0    0   0    0 | 1080   *    *    *    *    * |   2   1    1    0    0   0   0   0   0 |  1  2   2   1   0   0  0  0  0 | 1  1  2  0 0
xo3ox .. .. ..    ..&#x   3   3 |   3   6    3 |   1   3    3   1    0 |    * 720    *    *    *    *    0   0    6    0    0   0   0   0   0 |  0  0   6   3   0   0  0  0  0 | 0  2  3  0 0
.. ox3oo .. ..    ..&#x   1   3 |   0   3    3 |   0   0    3   0    1 |    *   * 4320    *    *    * |   0   0    1    2    1   0   0   0   0 |  0  0   2   1   1   2  0  0  0 | 0  1  2  1 0
.o3.x3.o .. ..    ..      0   6 |   0   0   12 |   0   0    0   4    4 |    *   *    * 1080    *    * |   0   0    1    0    0   2   1   0   0 |  0  0   2   1   0   0  1  2  0 | 0  1  2  0 1
.. .x3.o3.o ..    ..      0   4 |   0   0    6 |   0   0    0   0    4 |    *   *    *    * 2160    * |   0   0    0    1    0   1   0   1   1 |  0  0   1   0   1   1  1  1  1 | 0  1  1  1 1
.. .x3.o .. .. *c3.o      0   4 |   0   0    6 |   0   0    0   0    4 |    *   *    *    *    * 1080 |   0   0    0    0    1   0   1   0   2 |  0  0   0   1   0   2  0  2  1 | 0  0  2  1 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x.3o.3o.3o. ..    ..      5   0 |  10   0    0 |  10   0    0   0    0 |    5   0    0    0    0    0 | 432   *    *    *    *   *   *   *   * |  1  1   1   0   0   0  0  0  0 | 1  1  1  0 0
x.3o.3o. .. .. *c3o.      5   0 |  10   0    0 |  10   0    0   0    0 |    5   0    0    0    0    0 |   * 216    *    *    *   *   *   *   * |  0  2   0   1   0   0  0  0  0 | 1  0  2  0 0
xo3ox3oo .. ..    ..&#x   4   6 |   6  12   12 |   4   6   12   4    4 |    1   4    4    1    0    0 |   *   * 1080    *    *   *   *   *   * |  0  0   2   1   0   0  0  0  0 | 0  1  2  0 0
.. ox3oo3oo ..    ..&#x   1   4 |   0   4    6 |   0   0    6   0    4 |    0   0    4    0    1    0 |   *   *    * 2160    *   *   *   *   * |  0  0   1   0   1   1  0  0  0 | 0  1  1  1 0
.. ox3oo .. .. *c3oo&#x   1   4 |   0   4    6 |   0   0    6   0    4 |    0   0    4    0    0    1 |   *   *    *    * 1080   *   *   *   * |  0  0   0   1   0   2  0  0  0 | 0  0  2  1 0
.o3.x3.o3.o ..    ..      0  10 |   0   0   30 |   0   0    0  10   20 |    0   0    0    5    5    0 |   *   *    *    *    * 432   *   *   * |  0  0   1   0   0   0  1  1  0 | 0  1  1  0 1
.o3.x3.o .. .. *c3.o      0  10 |   0   0   30 |   0   0    0  10   20 |    0   0    0    5    0    5 |   *   *    *    *    *   * 216   *   * |  0  0   0   1   0   0  0  2  0 | 0  0  2  0 1
.. .x3.o3.o3.o    ..      0   5 |   0   0   10 |   0   0    0   0   10 |    0   0    0    0    5    0 |   *   *    *    *    *   *   * 432   * |  0  0   0   0   1   0  1  0  1 | 0  1  0  1 1
.. .x3.o3.o .. *c3.o      0   8 |   0   0   24 |   0   0    0   0   32 |    0   0    0    0    8    8 |   *   *    *    *    *   *   *   * 270 |  0  0   0   0   0   1  0  1  1 | 0  0  1  1 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x.3o.3o.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   0   0 | 72  *   *   *   *   *  *  *  * | 1  1  0  0 0
x.3o.3o.3o. .. *c3o.     10   0 |  40   0    0 |  80   0    0   0    0 |   80   0    0    0    0    0 |  16  16    0    0    0   0   0   0   0 |  * 27   *   *   *   *  *  *  * | 1  0  1  0 0
xo3ox3oo3oo ..    ..&#x   5  10 |  10  20   30 |  10  10   30  10   20 |    5  10   20    5    5    0 |   1   0    5    5    0   1   0   0   0 |  *  * 432   *   *   *  *  *  * | 0  1  1  0 0
xo3ox3oo .. .. *c3oo&#x   5  10 |  10  20   30 |  10  10   30  10   20 |    5  10   20    5    0    5 |   0   1    5    0    5   0   1   0   0 |  *  *   * 216   *   *  *  *  * | 0  0  2  0 0
.. ox3oo3oo3oo    ..&#x   1   5 |   0   5   10 |   0   0   10   0   10 |    0   0   10    0    5    0 |   0   0    0    5    0   0   0   1   0 |  *  *   *   * 432   *  *  *  * | 0  1  0  1 0
.. ox3oo3oo .. *c3oo&#x   1   8 |   0   8   24 |   0   0   24   0   32 |    0   0   32    0    8    8 |   0   0    0    8    8   0   0   0   1 |  *  *   *   *   * 270  *  *  * | 0  0  1  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    0    0    0   6   0   6   0 |  *  *   *   *   *   * 72  *  * | 0  1  0  0 1
.o3.x3.o3.o .. *c3.o      0  40 |   0   0  240 |   0   0    0  80  320 |    0   0    0   80   80   80 |   0   0    0    0    0  16  16   0  10 |  *  *   *   *   *   *  * 27  * | 0  0  1  0 1
.. .x3.o3.o3.o *c3.o      0  16 |   0   0   80 |   0   0    0   0  160 |    0   0    0    0   80   40 |   0   0    0    0    0   0   0  16  10 |  *  *   *   *   *   *  *  * 27 | 0  0  0  1 1
------------------------+--------+--------------+-----------------------+------------------------------+----------------------------------------+--------------------------------+-------------
x.3o.3o.3o.3o. *c3o.     27   0 | 216   0    0 | 720   0    0   0    0 | 1080   0    0    0    0    0 | 432 216    0    0    0   0   0   0   0 | 72 27   0   0   0   0  0  0  0 | 1  *  *  * *
xo3ox3oo3oo3oo    ..&#x   6  15 |  15  30   60 |  20  15   60  20   60 |   15  20   60   15   30    0 |   6   0   15   30    0   6   0   6   0 |  1  0   6   0   6   0  1  0  0 | * 72  *  * *
xo3ox3oo3oo .. *c3oo&#x  10  40 |  40  80  240 |  80  40  240  80  320 |   80  80  320   80   80   80 |  16  16   80   80   80  16  16   0  10 |  0  1  16  16   0  10  0  1  0 | *  * 27  * *
.. ox3oo3oo3oo *c3oo&#x   1  16 |   0  16   80 |   0   0   80   0  160 |    0   0  160    0   80   40 |   0   0    0   80   40   0   0  16  10 |  0  0   0   0  16  10  0  0  1 | *  *  * 27 *
.o3.x3.o3.o3.o *c3.o      0 216 |   0   0 2160 |   0   0    0 720 4320 |    0   0    0 1080 2160 1080 |   0   0    0    0    0 432 216 432 270 |  0  0   0   0   0   0 72 27 27 | *  *  *  * 1

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