This is a scaliform variant of a faceting of a Grünbaumian double-cover of the prismatorhombated hexadecachoron (proh). It comes out to be edge-inscribable to the rectified icositetrachora (rico). The additional 64 hexagons are the diametrals of two tesseractic subgroups of the former cuboctahedra (co), the additional 128 triangles are used to produce a quadruple coincidence of the former triangles of the remaining subgroup.

Incidence matrix according to Dynkin symbol

x3o3β4β

both( . . . . ) | 192 |   2   2   4 |  1  1  2  2   4   3 |  1  2 1  3
----------------+-----+-------------+---------------------+-----------
both( x . . . ) |   2 | 192   *   * |  1  0  0  1   2   0 |  1  1 0  2
sefa( . o3β . ) |   2 |   * 192   * |  0  1  0  1   0   1 |  1  0 1  1
sefa( . . s4s ) |   2 |   *   * 384 |  0  0  1  0   1   1 |  0  1 1  1
----------------+-----+-------------+---------------------+-----------
both( x3o . . ) |   3 |   3   0   0 | 64  *  *  *   *   * |  1  0 0  1
      . o3β .   ♦   3 |   0   3   0 |  * 64  *  *   *   * |  1  0 1  0
both( . . s4s ) ♦   4 |   0   0   4 |  *  * 96  *   *   * |  0  1 1  0
sefa( x3o3β . ) |   6 |   3   3   0 |  *  *  * 64   *   * |  1  0 0  1
sefa( x 2 s4s ) |   4 |   2   0   2 |  *  *  *  * 192   * |  0  1 0  1
sefa( . o3β4β ) |   3 |   0   1   2 |  *  *  *  *   * 192 |  0  0 1  1
----------------+-----+-------------+---------------------+-----------
      x3o3β .   ♦  12 |  12  12   0 |  4  4  0  4   0   0 | 16  * *  *
both( x 2 s4s ) ♦   8 |   4   0   8 |  0  0  2  0   4   0 |  * 48 *  *
      . o3β4β   ♦  24 |   0  24  48 |  0  8 12  0   0  24 |  *  * 8  *
sefa( x3o3β4β ) ♦   9 |   6   3   6 |  1  0  0  1   3   3 |  *  * * 64

starting figure: x3o3x4x