This polyotton is just the degenerate segmentotope of a crosspolytope atop a demihypercube. It either can be constructed as the tegum sum of ek and hocto or alternatively by augmentation of the all the 16 hesa facets of hocto by according pyramids.

Incidence matrix according to Dynkin symbol

xo3oo3oo *b3oo3oo3oo3oo3ox&#zx   → height = 0
(tegum sum of ek and hocto)

o.3o.3o. *b3o.3o.3o.3o.3o.     | 128  * |   28    8 |  168   168 |   56  280   840 |   70  280  280  1120 |  56  168  280   840 |  28   56  168  336 |   8  56   56
.o3.o3.o *b3.o3.o3.o3.o3.o     |   * 16 ♦    0   64 |    0   672 |    0    0  2240 |    0    0  560  2240 |   0    0  280  1344 |   0    0   84  448 |   0  14   64
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x. .. ..    .. .. .. .. ..     |   2  0 | 1792    * |   12     6 |    6   30    60 |   15   40   30   120 |  20   30   60   120 |  15   12   60   60 |   2  30   12
oo3oo3oo *b3oo3oo3oo3oo3oo&#x  |   1  1 |    * 1024 ♦    0    21 |    0    0   105 |    0    0   35   140 |   0    0   35   105 |   0    0   21   42 |   0   7    7
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o. ..    .. .. .. .. ..     |   3  0 |    3    0 | 7168     * |    1    5     5 |    5   10    5    20 |  10   10   20    30 |  10    5   30   20 |   1  20    5
xo .. ..    .. .. .. .. ..&#x  |   2  1 |    1    2 |    * 10752 ♦    0    0    10 |    0    0    5    20 |   0    0   10    20 |   0    0   10   10 |   0   5    2
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o.3o.    .. .. .. .. ..     ♦   4  0 |    6    0 |    4     0 | 1792    *     * |    5    0    5     0 |  10    0   20     0 |  10    0   30    0 |   0  20    0
x.3o. .. *b3o. .. .. .. ..     ♦   4  0 |    6    0 |    4     0 |    * 8960     * |    1    4    0     4 |   4    6    4    12 |   6    4   12   12 |   1  12    4
xo3oo ..    .. .. .. .. ..&#x  ♦   3  1 |    3    3 |    1     3 |    *    * 35840 |    0    0    1     4 |   0    0    4     6 |   0    0    6    4 |   0   4    1
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o.3o. *b3o. .. .. .. ..     ♦   8  0 |   24    0 |   32     0 |    8    8     0 | 1120    *    *     * |   4    0    4     0 |   6    0   12    0 |   0  12    0
x.3o. .. *b3o.3o. .. .. ..     ♦   5  0 |   10    0 |   10     0 |    0    5     0 |    * 7168    *     * |   1    3    0     3 |   3    3    3    6 |   1   6    3
xo3oo3oo    .. .. .. .. ..&#x  ♦   4  1 |    6    4 |    4     6 |    1    0     4 |    *    * 8960     * |   0    0    4     0 |   0    0    6    0 |   0   4    0
xo3oo .. *b3oo .. .. .. ..&#x  ♦   4  1 |    6    4 |    4     6 |    0    1     4 |    *    *    * 35840 |   0    0    1     3 |   0    0    3    3 |   0   3    1
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o.3o. *b3o.3o. .. .. ..     ♦  16  0 |   80    0 |  160     0 |   40   80     0 |   10   16    0     0 | 448    *    *     * |   3    0    3    0 |   0   6    0
x.3o. .. *b3o.3o.3o. .. ..     ♦   6  0 |   15    0 |   20     0 |    0   15     0 |    0    6    0     0 |   * 3584    *     * |   1    2    0    2 |   1   2    2
xo3oo3oo *b3oo .. .. .. ..&#x  ♦   8  1 |   24    8 |   32    24 |    8    8    32 |    1    0    8     8 |   *    * 4480     * |   0    0    3    0 |   0   3    0
xo3oo .. *b3oo3oo .. .. ..&#x  ♦   5  1 |   10    5 |   10    10 |    0    5    10 |    0    1    0     5 |   *    *    * 21504 |   0    0    1    2 |   0   2    1
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o.3o. *b3o.3o.3o. .. ..     ♦  32  0 |  240    0 |  640     0 |  160  480     0 |   60  192    0     0 |  12   32    0     0 | 112    *    *    * |   0   2    0
x.3o. .. *b3o.3o.3o.3o. ..     ♦   7  0 |   21    0 |   35     0 |    0   35     0 |    0   21    0     0 |   0    7    0     0 |   * 1024    *    * |   1   0    1
xo3oo3oo *b3oo3oo .. .. ..&#x  ♦  16  1 |   80   16 |  160    80 |   40   80   160 |   10   16   40    80 |   1    0   10    16 |   *    * 1344    * |   0   2    0
xo3oo .. *b3oo3oo3oo .. ..&#x  ♦   6  1 |   15    6 |   20    15 |    0   15    20 |    0    6    0    15 |   0    1    0     6 |   *    *    * 7168 |   0   1    1
-------------------------------+--------+-----------+------------+-----------------+----------------------+---------------------+--------------------+-------------
x.3o. .. *b3o.3o.3o.3o.3o.     ♦   8  0 |   28    0 |   56     0 |    0   70     0 |    0   56    0     0 |   0   28    0     0 |   0    8    0    0 | 128   *    *
xo3oo3oo *b3oo3oo3oo .. ..&#x  ♦  32  1 |  240   32 |  640   240 |  160  480   640 |   60  192  160   480 |  12   32   60   192 |   1    0   12   32 |   * 224    *
xo3oo .. *b3oo3oo3oo3oo ..&#x  ♦   7  1 |   21    7 |   35    21 |    0   35    35 |    0   21    0    35 |   0    7    0    21 |   0    1    0    7 |   *   * 1024