R         
       /  \\       
     /  |  \ \     
   /    _ - S_ \   
 / _ - |    |  -_\ 
T _           _ - T
 \  -_|  _ +     / 
   \  S        /   
     \ \  |  /     
       \\  /       
         R         

where:
R = x3o3x *b3o (rit)
S = x3o3o *b3x (+gyro rit)
T = o3o3x *b3x (-gyro rit)

When considering the lace hyper city of lin, then this polyexon can be spotted directly as the central R,S,T-octahedron of position space.

Incidence matrix according to Dynkin symbol

xoo oxo oox xxo3ooo3xox *e3oxx&#zx   → all heights = 0
(tegum sum of 3 mutually gyrated, lacings-orthogonal rittips)

o.. o.. o.. o..3o..3o.. *e3o..     & | 192 |  1   6   12 |   6   3   18   24   36  12 |  3  2   6   24  12   36  16  12   24   60 | 1   6  10  16  12  4  15   36  28   48 |  2  4  3  18  16  20  12 |  3  7 8
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
x.. ... ... ... ... ...    ...     & |   2 | 96   *    * |   0   0   12    0    0   0 |  0  0   6   12   0    0   0   0   12    0 | 0   6   4   0   0  0  12   12   0    0 |  2  0  3  12   4   0   0 |  3  4 0
... ... ... x.. ... ...    ...     & |   2 |  * 576    * |   2   1    0    4    4   0 |  2  1   0    2   4   10   4   2    0    8 | 1   1   2  10   4  2   0    4   8   12 |  1  4  0   4   4  12   4 |  1  4 4
oo. oo. oo. oo.3oo.3oo. *e3oo.&#x  & |   2 |  *   * 1152 |   0   0    2    2    4   2 |  0  0   1    4   1    4   2   2    5   12 | 0   2   2   2   2  1   4   10   6   12 |  1  1  1   8   5   6   4 |  2  4 2
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
... ... ... x..3o.. ...    ...     & |   3 |  0   3    0 | 384   *    *    *    *   * |  1  1   0    0   2    0   2   0    0    0 | 1   0   1   6   0  2   0    0   4    0 |  1  4  0   0   2   8   0 |  0  3 4
... ... ... x.. ... x..    ...     & |   4 |  0   4    0 |   * 144    *    *    *   * |  2  0   0    0   0    8   0   0    0    0 | 1   0   0   8   4  0   0    0   0    8 |  0  4  0   2   0   8   4 |  1  2 4
xo. ... ... ... ... ...    ...&#x  & |   3 |  1   0    2 |   *   * 1152    *    *   * |  0  0   1    2   0    0   0   0    2    0 | 0   2   1   0   0  0   3    4   0    0 |  1  0  1   6   2   0   0 |  2  3 0
... ... ... xx. ... ...    ...&#x  & |   4 |  0   2    2 |   *   *    * 1152    *   * |  0  0   0    0   1    2   0   0    0    2 | 0   0   0   2   1  0   0    1   2    4 |  0  1  0   2   1   4   2 |  1  2 2
... ... ... ... ... xo.    ...&#x  & |   3 |  0   1    2 |   *   *    *    * 2304   * |  0  0   0    1   0    1   1   1    0    2 | 0   1   1   1   1  1   0    2   2    4 |  1  1  0   3   2   4   2 |  1  3 2
ooo ooo ooo ooo3ooo3ooo *e3ooo&#x    |   3 |  0   0    3 |   *   *    *    *    * 768 |  0  0   0    0   0    0   0   0    3    6 | 0   0   0   0   0  0   3    6   3    6 |  0  0  1   6   3   3   2 |  2  3 1
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
... ... ... x..3o..3x..    ...     & ♦  12 |  0  24    0 |   8   6    0    0    0   0 | 48  *   *    *   *    *   *   *    *    * | 1   0   0   4   0  0   0    0   0    0 |  0  4  0   0   0   4   0 |  0  1 4
... ... ... x..3o.. ... *e3o..     & ♦   4 |  0   6    0 |   4   0    0    0    0   0 |  * 96   *    *   *    *   *   *    *    * | 1   0   0   2   0  2   0    0   0    0 |  1  4  0   0   0   4   0 |  0  2 4
xo. ox. ... ... ... ...    ...&#x  & ♦   4 |  2   0    4 |   0   0    4    0    0   0 |  *  * 288    *   *    *   *   *    *    * | 0   2   0   0   0  0   2    0   0    0 |  1  0  1   4   0   0   0 |  2  2 0
xo. ... ... ... ... ...    ox.&#x  & ♦   4 |  1   1    4 |   0   0    2    0    2   0 |  *  *   * 1152   *    *   *   *    *    * | 0   1   1   0   0  0   0    2   0    0 |  1  0  0   3   2   0   0 |  1  3 0
... ... ... xx.3oo. ...    ...&#x  & ♦   6 |  0   6    3 |   2   0    0    3    0   0 |  *  *   *    * 384    *   *   *    *    * | 0   0   0   2   0  0   0    0   2    0 |  0  1  0   0   1   4   0 |  0  2 2
... ... ... xx. ... xo.    ...&#x  & ♦   6 |  0   5    4 |   0   1    0    2    2   0 |  *  *   *    *   * 1152   *   *    *    * | 0   0   0   1   1  0   0    0   0    2 |  0  1  0   1   0   2   2 |  1  1 2
... ... ... ... oo.3xo.    ...&#x  & ♦   4 |  0   3    3 |   1   0    0    0    3   0 |  *  *   *    *   *    * 768   *    *    * | 0   0   1   1   0  1   0    0   2    0 |  1  1  0   0   2   4   0 |  0  3 2
... ... ... ... ... xo.    ox.&#x  & ♦   4 |  0   2    4 |   0   0    0    0    4   0 |  *  *   *    *   *    *   * 576    *    * | 0   1   0   0   1  1   0    0   0    2 |  1  1  0   2   0   2   2 |  1  2 2
xoo ... ... ... ... ...    ...&#x  & ♦   4 |  1   0    5 |   0   0    2    0    0   2 |  *  *   *    *   *    *   *   * 1152    * | 0   0   0   0   0  0   2    2   0    0 |  0  0  1   4   1   0   0 |  2  2 0
... ... ... xxo ... ...    ...&#x  & ♦   5 |  0   2    6 |   0   0    0    1    2   2 |  *  *   *    *   *    *   *   *    * 2304 | 0   0   0   0   0  0   0    1   1    2 |  0  0  0   2   1   2   1 |  1  2 1
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
... ... ... x..3o..3x.. *e3o..     & ♦  32 |  0  96    0 |  64  24    0    0    0   0 |  8 16   0    0   0    0   0   0    0    0 | 6   *   *   *   *  *   *    *   *    * |  0  4  0   0   0   0   0 |  0  0 4
xo. ox. ... ... ... xo.    ox.&#zx & ♦   8 |  4   4   16 |   0   0   16    0   16   0 |  0  0   4    8   0    0   0   4    0    0 | * 144   *   *   *  *   *    *   *    * |  1  0  0   2   0   0   0 |  1  2 0
xo. ... ... ... oo. ... *e3ox.&#x  & ♦   5 |  1   3    6 |   1   0    3    0    6   0 |  0  0   0    3   0    0   2   0    0    0 | *   * 384   *   *  *   *    *   *    * |  1  0  0   0   2   0   0 |  0  3 0
... ... ... xx.3oo.3xo.    ...&#x  & ♦  16 |  0  30   12 |  12   6    0   12   12   0 |  1  1   0    0   4    6   4   0    0    0 | *   *   * 192   *  *   *    *   *    * |  0  1  0   0   0   2   0 |  0  1 2
... ... ... xx. ... xo.    ox.&#x  & ♦   8 |  0   8    8 |   0   2    0    4    8   0 |  0  0   0    0   0    4   0   2    0    0 | *   *   *   * 288  *   *    *   *    * |  0  1  0   0   0   0   2 |  1  0 2
... ... ... ... oo.3xo. *e3ox.&#x  & ♦   8 |  0  12   12 |   8   0    0    0   24   0 |  0  2   0    0   0    0   8   6    0    0 | *   *   *   *   * 96   *    *   *    * |  1  1  0   0   0   2   0 |  0  2 2
xoo oxo ... ... ... ...    ...&#x  & ♦   5 |  2   0    8 |   0   0    6    0    0   4 |  0  0   1    0   0    0   0   0    4    0 | *   *   *   *   *  * 576    *   *    * |  0  0  1   2   0   0   0 |  2  1 0
xoo ... ... ... ... ...    oxx&#x  & ♦   6 |  1   2   10 |   0   0    4    1    4   4 |  0  0   0    2   0    0   0   0    2    2 | *   *   *   *   *  *   * 1152   *    * |  0  0  0   2   1   0   0 |  1  2 0
... ... ... xxo3ooo ...    ...&#x  & ♦   7 |  0   6    9 |   2   0    0    3    6   3 |  0  0   0    0   1    0   2   0    0    3 | *   *   *   *   *  *   *    * 768    * |  0  0  0   0   1   2   0 |  0  2 1
... ... ... xxo ... xox    ...&#x  & ♦   8 |  0   6   12 |   0   1    0    4    8   4 |  0  0   0    0   0    2   0   1    0    4 | *   *   *   *   *  *   *    *   * 1152 |  0  0  0   1   0   1   1 |  1  1 1
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
xo. ox. ... ... oo.3xo. *e3ox.&#zx & ♦  16 |  8  24   48 |  16   0   48    0   96   0 |  0  4  12   48   0    0  32  24    0    0 | 0   6  16   0   0  4   0    0   0    0 | 24  *  *   *   *   *   * |  0  2 0
... ... ... xx.3oo.3xo. *e3ox.&#x  & ♦  64 |  0 192   96 | 128  48    0   96  192   0 | 16 32   0    0  32   96  64  48    0    0 | 2   0   0  16  24  8   0    0   0    0 |  * 12  *   *   *   *   * |  0  0 2
xoo oxo oox ... ... ...    ...&#x    ♦   6 |  3   0   12 |   0   0   12    0    0   8 |  0  0   3    0   0    0   0   0   12    0 | 0   0   0   0   0  0   6    0   0    0 |  *  * 96   *   *   *   * |  2  0 0
xoo oxo ... ... ... xox    oxx&#x  & ♦  12 |  4   8   32 |   0   1   24    8   24  16 |  0  0   4   12   0    4   0   4   16   16 | 0   1   0   0   0  0   4    8   0    4 |  *  *  * 288   *   *   * |  1  1 0
xoo ... ... ... ooo ... *e3oxx&#x  & ♦   8 |  1   6   15 |   2   0    6    3   12   6 |  0  0   0    6   1    0   4   0    3    6 | 0   0   2   0   0  0   0    3   2    0 |  *  *  *   * 384   *   * |  0  2 0
... ... ... xxo3ooo3xox    ...&#x  & ♦  20 |  0  36   36 |  16   6    0   24   48  12 |  1  2   0    0   8   12  16   6    0   24 | 0   0   0   2   0  1   0    0   8    6 |  *  *  *   *   * 192   * |  0  1 1
... ... ... xxo ... xox    oxx&#x    ♦  12 |  0  12   24 |   0   3    0   12   24   8 |  0  0   0    0   0   12   0   6    0   12 | 0   0   0   0   3  0   0    0   0    6 |  *  *  *   *   *   * 192 |  1  0 1
-------------------------------------+-----+-------------+----------------------------+-------------------------------------------+----------------------------------------+--------------------------+--------
xoo oxo oox xxo ... xox    oxx&#zx   ♦  24 | 12  24   96 |   0   6   96   48   96  64 |  0  0  24   48   0   48   0  24   96   96 | 0   6   0   0  12  0  48   48   0   48 |  0  0  8  12   0   0   8 | 24  * *
xoo oxo ... ... ooo3xox *e3oxx&#x  & ♦  28 |  8  48   96 |  24   6   72   48  144  48 |  1  4  12   72  16   24  48  24   48   96 | 0   6  24   4   0  4  12   48  32   24 |  1  0  0   6  16   4   0 |  * 48 *  as (AB)-C lace prism
... ... ... xxo3ooo3xox *e3oxx&#x    ♦  96 |  0 288  288 | 192  72    0  288  576  96 | 24 48   0    0  96  288 192 144    0  288 | 3   0   0  48  72 24   0    0  96  144 |  0  3  0   0   0  24  24 |  *  * 8