This polyexon is obtained from spox within its C₃ × C₃ subsymmetry, then becoming ooxo3oxoo4wxxx oxox3ooxx4xxxw&#zx, by removing the first and last component thereof, i.e. by removing 2 alternate cubic duoprisms o3o4x o3o4w; each of which has 8 × 8 = 64 vertices, thence its name.

Incidence matrix according to Dynkin symbol

xo3ox4xx ox3xo4xx&#zx   → height = 0
(tegum sum of 2 alt. sircotics)

o.3o.4o. o.3o.4o.     & | 1152 |    2    2    2   1    4 |   1   2    4   2   1    4   2   1    6    6    8 |  1   2   1   4   2   2   2   1   2   4    6   2    5    6   2    6   4 |  2  1   1   2  1   3   3   4   4   5   6  2 |  1  3  1   3   2
------------------------+------+-------------------------+--------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------+-----------------
x. .. .. .. .. ..     & |    2 | 1152    *    *   *    * |   1   1    2   1   0    0   0   0    2    0    0 |  1   2   1   2   1   1   0   0   0   2    2   1    2    2   0    0   0 |  2  1   1   1  0   2   2   2   2   2   2  0 |  1  2  1   2   1
.. .. x. .. .. ..     & |    2 |    * 1152    *   *    * |   0   1    0   0   1    2   1   0    0    0    2 |  1   0   0   2   1   0   2   1   1   0    2   0    0    1   0    2   2 |  2  1   0   1  1   0   0   1   1   2   3  2 |  1  3  0   1   1
.. .. .. .. x. ..     & |    2 |    *    * 1152   *    * |   0   0    2   0   0    2   0   1    0    2    0 |  0   1   0   2   0   2   1   0   2   2    0   0    2    0   1    2   0 |  1  0   1   2  1   2   2   2   0   2   0  1 |  1  2  1   2   0
.. .. .. .. .. x.     & |    2 |    *    *    * 576    * |   0   0    0   2   0    0   2   0    0    0    4 |  0   0   1   0   2   0   0   1   0   0    2   0    0    4   0    2   4 |  0  1   0   0  0   0   0   2   2   1   6  2 |  0  3  0   1   2
oo3oo4oo oo3oo4oo&#x    |    2 |    *    *    *   * 2304 |   0   0    0   0   0    0   0   0    2    2    2 |  0   0   0   0   0   0   0   0   0   2    2   1    2    2   1    2   1 |  0  0   0   0  0   2   2   2   2   2   2  1 |  0  2  1   2   1
------------------------+------+-------------------------+--------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------+-----------------
x.3o. .. .. .. ..     & |    3 |    3    0    0   0    0 | 384   *    *   *   *    *   *   *    *    *    * |  1   2   1   0   0   0   0   0   0   2    0   0    0    0   0    0   0 |  2  1   1   0  0   1   2   2   0   0   0  0 |  1  2  1   1   0
x. .. x. .. .. ..     & |    4 |    2    2    0   0    0 |   * 576    *   *   *    *   *   *    *    *    * |  1   0   0   2   1   0   0   0   0   0    2   0    0    0   0    0   0 |  2  1   0   1  0   0   0   0   1   2   2  0 |  1  2  0   1   1
x. .. .. .. x. ..     & |    4 |    2    0    2   0    0 |   *   * 1152   *   *    *   *   *    *    *    * |  0   1   0   1   0   1   0   0   0   0    0   0    1    0   0    0   0 |  1  0   1   1  0   1   1   0   0   1   0  0 |  1  1  1   1   0
x. .. .. .. .. x.     & |    4 |    2    0    0   2    0 |   *   *    * 576   *    *   *   *    *    *    * |  0   0   1   0   1   0   0   0   0   0    0   0    0    2   0    0   0 |  0  1   0   0  0   0   0   2   1   0   2  0 |  0  2  0   1   1
.. o.4x. .. .. ..     & |    4 |    0    4    0   0    0 |   *   *    *   * 288    *   *   *    *    *    * |  1   0   0   0   0   0   2   1   0   0    0   0    0    0   0    0   0 |  2  1   0   0  1   0   0   0   0   0   0  2 |  1  3  0   0   0
.. .. x. .. x. ..     & |    4 |    0    2    2   0    0 |   *   *    *   *   * 1152   *   *    *    *    * |  0   0   0   1   0   0   1   0   1   0    0   0    0    0   0    1   0 |  1  0   0   1  1   0   0   1   0   1   0  1 |  1  2  0   1   0
.. .. x. .. .. x.     & |    4 |    0    2    0   2    0 |   *   *    *   *   *    * 576   *    *    *    * |  0   0   0   0   1   0   0   1   0   0    0   0    0    0   0    0   2 |  0  1   0   0  0   0   0   0   0   0   3  2 |  0  3  0   0   1
.. .. .. o.3x. ..     & |    3 |    0    0    3   0    0 |   *   *    *   *   *    *   * 384    *    *    * |  0   0   0   0   0   2   0   0   2   2    0   0    0    0   0    0   0 |  0  0   1   2  1   2   1   2   0   0   0  0 |  1  1  1   2   0
xo .. .. .. .. ..&#x  & |    3 |    1    0    0   0    2 |   *   *    *   *   *    *   *   * 2304    *    * |  0   0   0   0   0   0   0   0   0   1    1   1    1    1   0    0   0 |  0  0   0   0  0   2   1   1   2   1   1  0 |  0  1  1   2   1
.. ox .. .. .. ..&#x  & |    3 |    0    0    1   0    2 |   *   *    *   *   *    *   *   *    * 2304    * |  0   0   0   0   0   0   0   0   0   1    0   0    1    0   1    1   0 |  0  0   0   0  0   1   2   1   0   1   0  1 |  0  2  1   1   0
.. .. xx .. .. ..&#x  & |    4 |    0    1    0   1    2 |   *   *    *   *   *    *   *   *    *    * 2304 |  0   0   0   0   0   0   0   0   0   0    1   0    0    1   0    1   1 |  0  0   0   0  0   0   0   1   1   1   2  1 |  0  2  0   1   1
------------------------+------+-------------------------+--------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------+-----------------
x.3o.4x. .. .. ..     & ♦   24 |   24   24    0   0    0 |   8  12    0   0   6    0   0   0    0    0    0 | 48   *   *   *   *   *   *   *   *   *    *   *    *    *   *    *   * |  2  1   0   0  0   0   0   0   0   0   0  0 |  1  2  0   0   0
x.3o. .. .. x. ..     & ♦    6 |    6    0    3   0    0 |   2   0    3   0   0    0   0   0    0    0    0 |  * 384   *   *   *   *   *   *   *   *    *   *    *    *   *    *   * |  1  0   1   0  0   0   1   0   0   0   0  0 |  1  1  1   0   0
x.3o. .. .. .. x.     & ♦    6 |    6    0    0   3    0 |   2   0    0   3   0    0   0   0    0    0    0 |  *   * 192   *   *   *   *   *   *   *    *   *    *    *   *    *   * |  0  1   0   0  0   0   0   2   0   0   0  0 |  0  2  0   1   0
x. .. x. .. x. ..     & ♦    8 |    4    4    4   0    0 |   0   2    2   0   0    2   0   0    0    0    0 |  *   *   * 576   *   *   *   *   *   *    *   *    *    *   *    *   * |  1  0   0   1  0   0   0   0   0   1   0  0 |  1  1  0   1   0
x. .. x. .. .. x.     & ♦    8 |    4    4    0   4    0 |   0   2    0   2   0    0   2   0    0    0    0 |  *   *   *   * 288   *   *   *   *   *    *   *    *    *   *    *   * |  0  1   0   0  0   0   0   0   0   0   2  0 |  0  2  0   0   1
x. .. .. o.3x. ..     & ♦    6 |    3    0    6   0    0 |   0   0    3   0   0    0   0   2    0    0    0 |  *   *   *   *   * 384   *   *   *   *    *   *    *    *   *    *   * |  0  0   1   1  0   1   0   0   0   0   0  0 |  1  0  1   1   0
.. o.4x. .. x. ..     & ♦    8 |    0    8    4   0    0 |   0   0    0   0   2    4   0   0    0    0    0 |  *   *   *   *   *   * 288   *   *   *    *   *    *    *   *    *   * |  1  0   0   0  1   0   0   0   0   0   0  1 |  1  2  0   0   0
.. o.4x. .. .. x.     & ♦    8 |    0    8    0   4    0 |   0   0    0   0   2    0   4   0    0    0    0 |  *   *   *   *   *   *   * 144   *   *    *   *    *    *   *    *   * |  0  1   0   0  0   0   0   0   0   0   0  2 |  0  3  0   0   0
.. .. x. o.3x. ..     & ♦    6 |    0    3    6   0    0 |   0   0    0   0   0    3   0   2    0    0    0 |  *   *   *   *   *   *   *   * 384   *    *   *    *    *   *    *   * |  0  0   0   1  1   0   0   1   0   0   0  0 |  1  1  0   1   0
xo3ox .. .. .. ..&#x  & ♦    6 |    3    0    3   0    6 |   1   0    0   0   0    0   0   1    3    3    0 |  *   *   *   *   *   *   *   *   * 768    *   *    *    *   *    *   * |  0  0   0   0  0   1   1   1   0   0   0  0 |  0  1  1   1   0
xo .. xx .. .. ..&#x  & ♦    6 |    2    2    0   1    4 |   0   1    0   0   0    0   0   0    2    0    2 |  *   *   *   *   *   *   *   *   *   * 1152   *    *    *   *    *   * |  0  0   0   0  0   0   0   0   1   1   1  0 |  0  1  0   1   1
xo .. .. ox .. ..&#x    ♦    4 |    2    0    0   0    4 |   0   0    0   0   0    0   0   0    4    0    0 |  *   *   *   *   *   *   *   *   *   *    * 576    *    *   *    *   * |  0  0   0   0  0   2   0   0   2   0   0  0 |  0  0  1   2   1
xo .. .. .. xo ..&#x  & ♦    5 |    2    0    2   0    4 |   0   0    1   0   0    0   0   0    2    2    0 |  *   *   *   *   *   *   *   *   *   *    *   * 1152    *   *    *   * |  0  0   0   0  0   1   1   0   0   1   0  0 |  0  1  1   1   0
xo .. .. .. .. xx&#x  & ♦    6 |    2    1    0   2    4 |   0   0    0   1   0    0   0   0    2    0    2 |  *   *   *   *   *   *   *   *   *   *    *   *    * 1152   *    *   * |  0  0   0   0  0   0   0   1   1   0   1  0 |  0  1  0   1   1
.. ox .. .. xo ..&#x    ♦    4 |    0    0    2   0    4 |   0   0    0   0   0    0   0   0    0    4    0 |  *   *   *   *   *   *   *   *   *   *    *   *    *    * 576    *   * |  0  0   0   0  0   0   2   0   0   0   0  1 |  0  2  1   0   0
.. ox .. .. .. xx&#x  & ♦    6 |    0    2    2   1    4 |   0   0    0   0   0    1   0   0    0    2    2 |  *   *   *   *   *   *   *   *   *   *    *   *    *    *   * 1152   * |  0  0   0   0  0   0   0   1   0   1   0  1 |  0  2  0   1   0
.. .. xx .. .. xx&#x    ♦    8 |    0    4    0   4    4 |   0   0    0   0   0    0   2   0    0    0    4 |  *   *   *   *   *   *   *   *   *   *    *   *    *    *   *    * 576 |  0  0   0   0  0   0   0   0   0   0   2  1 |  0  2  0   0   1
------------------------+------+-------------------------+--------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------+-----------------
x.3o.4x. .. x. ..     & ♦   48 |   48   48   24   0    0 |  16  24   24   0  12   24   0   0    0    0    0 |  2   8   0  12   0   0   6   0   0   0    0   0    0    0   0    0   0 | 48  *   *   *  *   *   *   *   *   *   *  * |  1  1  0   0   0
x.3o.4x. .. .. x.     & ♦   48 |   48   48    0  24    0 |  16  24    0  24  12    0  24   0    0    0    0 |  2   0   8   0  12   0   0   6   0   0    0   0    0    0   0    0   0 |  * 24   *   *  *   *   *   *   *   *   *  * |  0  2  0   0   0
x.3o. .. o.3x. ..     & ♦    9 |    9    0    9   0    0 |   3   0    9   0   0    0   0   3    0    0    0 |  0   3   0   0   0   3   0   0   0   0    0   0    0    0   0    0   0 |  *  * 128   *  *   *   *   *   *   *   *  * |  1  0  1   0   0
x. .. x. o.3x. ..     & ♦   12 |    6    6   12   0    0 |   0   3    6   0   0    6   0   4    0    0    0 |  0   0   0   3   0   2   0   0   2   0    0   0    0    0   0    0   0 |  *  *   * 192  *   *   *   *   *   *   *  * |  1  0  0   1   0
.. o.4x. o.3x. ..     & ♦   12 |    0   12   12   0    0 |   0   0    0   0   3   12   0   4    0    0    0 |  0   0   0   0   0   0   3   0   4   0    0   0    0    0   0    0   0 |  *  *   *   * 96   *   *   *   *   *   *  * |  1  1  0   0   0
xo3ox .. ox .. ..&#x  & ♦    9 |    6    0    6   0   12 |   1   0    3   0   0    0   0   2   12    6    0 |  0   0   0   0   0   1   0   0   0   2    0   3    3    0   0    0   0 |  *  *   *   *  * 384   *   *   *   *   *  * |  0  0  1   1   0
xo3ox .. .. xo ..&#x  & ♦    9 |    6    0    6   0   12 |   2   0    3   0   0    0   0   1    6   12    0 |  0   1   0   0   0   0   0   0   0   2    0   0    3    0   3    0   0 |  *  *   *   *  *   * 384   *   *   *   *  * |  0  1  1   0   0
xo3ox .. .. .. xx&#x  & ♦   12 |    6    3    6   3   12 |   2   0    0   3   0    3   0   2    6    6    6 |  0   0   1   0   0   0   0   0   1   2    0   0    0    3   0    3   0 |  *  *   *   *  *   *   * 384   *   *   *  * |  0  1  0   1   0
xo .. xx ox .. ..&#x  & ♦    8 |    4    2    0   2    8 |   0   1    0   1   0    0   0   0    8    0    4 |  0   0   0   0   0   0   0   0   0   0    2   2    0    2   0    0   0 |  *  *   *   *  *   *   *   * 576   *   *  * |  0  0  0   1   1
xo .. xx .. xo ..&#x  & ♦   10 |    4    4    4   1    8 |   0   2    2   0   0    2   0   0    4    4    4 |  0   0   0   1   0   0   0   0   0   0    2   0    2    0   0    2   0 |  *  *   *   *  *   *   *   *   * 576   *  * |  0  1  0   1   0
xo .. xx .. .. xx&#x  & ♦   12 |    4    6    0   6    8 |   0   2    0   2   0    0   3   0    4    0    8 |  0   0   0   0   1   0   0   0   0   0    2   0    0    2   0    0   2 |  *  *   *   *  *   *   *   *   *   * 576  * |  0  1  0   0   1
.. ox4xx .. xo4xx&#zx   ♦   64 |    0   64   32  32   64 |   0   0    0   0  16   32  32   0    0   64   64 |  0   0   0   0   0   0   8   8   0   0    0   0    0    0  16   32  16 |  *  *   *   *  *   *   *   *   *   *   * 36 |  0  2  0   0   0
------------------------+------+-------------------------+--------------------------------------------------+------------------------------------------------------------------------+---------------------------------------------+-----------------
x.3o.4x. o.3x. ..     & ♦   72 |   72   72   72   0    0 |  24  36   72   0  18   72   0  24    0    0    0 |  3  24   0  36   0  24  18   0  24   0    0   0    0    0   0    0   0 |  3  0   8  12  6   0   0   0   0   0   0  0 | 16  *  *   *   *
xo3ox4xx .. xo4xx&#zx & ♦  288 |  192  288  192 144  384 |  64  96   96  96  72  192 144  32  192  384  384 |  8  32  32  48  48   0  48  36  32  64   96   0   96   96  96  192  96 |  4  4   0   0  8   0  32  32   0  48  48  6 |  * 12  *   *   *
xo3ox .. ox3xo ..&#x    ♦   18 |   18    0   18   0   36 |   6   0   18   0   0    0   0   6   36   36    0 |  0   6   0   0   0   6   0   0   0  12    0   9   18    0   9    0   0 |  0  0   2   0  0   6   6   0   0   0   0  0 |  *  * 64   *   *
xo3ox .. ox .. xx&#x  & ♦   18 |   12    6   12   3   24 |   2   3    6   3   0    6   0   4   24   12   12 |  0   0   1   3   0   2   0   0   2   4    6   6    6    6   0    6   0 |  0  0   0   1  0   2   0   2   3   3   0  0 |  *  *  * 192   *
xo .. xx ox .. xx&#x    ♦   16 |    8    8    0   8   16 |   0   4    0   4   0    0   4   0   16    0   16 |  0   0   0   0   2   0   0   0   0   0    8   4    0    8   0    0   4 |  0  0   0   0  0   0   0   0   4   0   4  0 |  *  *  *   * 144