As abstract polytope getit cadoca is isomorphic to stut cadoca, thereby replacing octagons by octagrams, resp. socco by gocco and tic by quith.

Incidence matrix according to Dynkin symbol

x3o3o4/3x4*a3*c   (N,M → ∞)

. . .   .       | 8NM |    6    3 |   3   3   6   3 |  1  3  3  1
----------------+-----+-----------+-----------------+------------
x . .   .       |   2 | 24NM    * |   1   1   1   0 |  1  1  1  0
. . .   x       |   2 |    * 12NM |   0   0   2   2 |  0  1  2  1
----------------+-----+-----------+-----------------+------------
x3o .   .       |   3 |    3    0 | 8NM   *   *   * |  1  1  0  0
x . o   . *a3*c |   3 |    3    0 |   * 8NM   *   * |  1  0  1  0
x . .   x4*a    |   8 |    4    4 |   *   * 6NM   * |  0  1  1  0
. . o4/3x       |   4 |    0    4 |   *   *   * 6NM |  0  0  1  1
----------------+-----+-----------+-----------------+------------
x3o3o   . *a3*c ♦   M |   3M    0 |   M   M   0   0 | 8N  *  *  *
x3o .   x4*a    ♦  24 |   24   12 |   8   0   6   0 |  * NM  *  *
x . o4/3x4*a3*c ♦  24 |   24   24 |   0   8   6   6 |  *  * NM  *
. o3o4/3x       ♦   8 |    0   12 |   0   0   0   6 |  *  *  * NM

x3/2o3/2o4/3x4*a3*c   (N,M → ∞)

.   .   .   .       | 8NM |    6    3 |   3   3   6   3 |  1  3  3  1
--------------------+-----+-----------+-----------------+------------
x   .   .   .       |   2 | 24NM    * |   1   1   1   0 |  1  1  1  0
.   .   .   x       |   2 |    * 12NM |   0   0   2   2 |  0  1  2  1
--------------------+-----+-----------+-----------------+------------
x3/2o   .   .       |   3 |    3    0 | 8NM   *   *   * |  1  1  0  0
x   .   o   . *a3*c |   3 |    3    0 |   * 8NM   *   * |  1  0  1  0
x   .   .   x4*a    |   8 |    4    4 |   *   * 6NM   * |  0  1  1  0
.   .   o4/3x       |   4 |    0    4 |   *   *   * 6NM |  0  0  1  1
--------------------+-----+-----------+-----------------+------------
x3/2o3/2o   . *a3*c ♦   M |   3M    0 |   M   M   0   0 | 8N  *  *  *
x3/2o   .   x4*a    ♦  24 |   24   12 |   8   0   6   0 |  * NM  *  *
x   .   o4/3x4*a3*c ♦  24 |   24   24 |   0   8   6   6 |  *  * NM  *
.   o3/2o4/3x       ♦   8 |    0   12 |   0   0   0   6 |  *  *  * NM