As abstract polytope gikkivcadach is isomorphic to skivcadach, thereby replacing octagons by octagrams, resp. socco by gocco, girco by quitco, and querco by sirco.

Incidence matrix according to Dynkin symbol

x3x3o4/3x4*a3*c   (N,M → ∞)

. . .   .       | 24NM |    2    2    2 |   2   1   2   1    2   1 |  1  2  1  1
----------------+------+----------------+--------------------------+------------
x . .   .       |    2 | 24NM    *    * |   1   1   1   0    0   0 |  1  1  1  0
. x .   .       |    2 |    * 24NM    * |   1   0   0   1    1   0 |  1  1  0  1
. . .   x       |    2 |    *    * 24NM |   0   0   1   0    1   1 |  0  1  1  1
----------------+------+----------------+--------------------------+------------
x3x .   .       |    6 |    3    3    0 | 8NM   *   *   *    *   * |  1  1  0  0
x . o   . *a3*c |    3 |    3    0    0 |   * 8NM   *   *    *   * |  1  0  1  0
x . .   x4*a    |    8 |    4    0    4 |   *   * 6NM   *    *   * |  0  1  1  0
. x3o   .       |    3 |    0    3    0 |   *   *   * 8NM    *   * |  1  0  0  1
. x .   x       |    4 |    0    2    2 |   *   *   *   * 12NM   * |  0  1  0  1
. . o4/3x       |    4 |    0    0    4 |   *   *   *   *    * 6NM |  0  0  1  1
----------------+------+----------------+--------------------------+------------
x3x3o   . *a3*c ♦   3M |   3M   3M    0 |   M   M   0   M    0   0 | 8N  *  *  *
x3x .   x4*a    ♦   48 |   24   24   24 |   8   0   6   0   12   0 |  * NM  *  *
x . o4/3x4*a3*c ♦   24 |   24    0   24 |   0   8   6   0    0   6 |  *  * NM  *
. x3o4/3x       ♦   24 |    0   24   24 |   0   0   0   8   12   6 |  *  *  * NM