It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.

Incidence matrix according to Dynkin symbol

pt || cho   → height = 0

  1  * ♦ 12  0 | 24 0 0 | 6 4 0
  * 12 |  1  4 |  4 2 2 | 2 2 1
  -----+-------+--------+------
  1  1 | 12  * |  4 0 0 | 2 2 0
  0  2 |  * 24 |  1 1 1 | 1 1 1
  -----+-------+--------+------
  1  2 |  2  1 | 24 * * | 1 1 0
  0  4 |  0  4 |  * 6 * | 1 0 1
  0  6 |  0  6 |  * * 4 | 0 1 1
  -----+-------+--------+------
♦ 1  4 |  4  4 |  4 1 0 | 6 * *
♦ 1  6 |  6  6 |  6 0 1 | * 4 *
♦ 0 12 |  0 24 |  0 6 4 | * * 1