Incidence matrix

1440 |   1   10 |   10   10   10 |   10   10   10   2 |  10   2 1
-----+----------+----------------+--------------------+----------
   2 | 720    * |   10    0    0 |   10   10    0   0 |  10   2 0  lacing edges
   2 |   * 7200 |    1    2    2 |    2    2    3   1 |   3   1 1  base edges
-----+----------+----------------+--------------------+----------
   4 |   2    2 | 3600    *    * |    2    2    0   0 |   3   1 0
   4 |   0    4 |    * 3600    * |    1    0    2   0 |   2   0 1
   5 |   0    5 |    *    * 2880 |    0    1    1   1 |   1   1 1
-----+----------+----------------+--------------------+----------
   8 |   4    8 |    4    2    0 | 1800    *    *   * |   2   0 0  cube
  10 |   5   10 |    5    0    2 |    * 1440    *   * |   1   1 0  pip
  10 |   0   15 |    0    5    2 |    *    * 1440   * |   1   0 1  pip
  12 |   0   30 |    0    0   12 |    *    *    * 240 |   0   1 1  gad
-----+----------+----------------+--------------------+----------
  20 |  10   30 |   15   10    4 |    5    2    2   0 | 720   * *  squipdip
  24 |  12   60 |   30    0   24 |    0   12    0   2 |   * 120 *  gaddip
 720 |   0 3600 |    0 1800 1440 |    0    0  720 120 |   *   * 2  sophi