This is a scaliform variant of a faceting of a Grünbaumian double-cover of the prismatorhombated icositetrachoron (prico). It comes out to be edge-inscribable to the small rhombated icositetrachoron (srico). The additional 144 octagons are those inscribed into the former small rhombicuboctahedra (sirco), the additional 576 triangles are used to produce a octuple coincidence of the former sirco-sirco triangles.

Incidence matrix according to Dynkin symbol

β3x4o3β

both( . . . .    ) | 576 |   2   2   2   2 |   1   2   1   1   4   3   2 |  1  2  2  1   3
-------------------+-----+-----------------+-----------------------------+----------------
both( . x . .    ) |   2 | 576   *   *   * |   1   1   0   0   1   0   1 |  1  1  0  1   1
both( s . . s2*a ) |   2 |   * 576   *   * |   0   0   0   0   2   2   0 |  0  1  1  0   2
sefa( β3x . .    ) |   2 |   *   * 576   * |   0   1   0   1   1   0   0 |  1  1  0  0   1
sefa( . . o3β    ) |   2 |   *   *   * 576 |   0   0   1   0   0   1   1 |  0  0  1  1   1
-------------------+-----+-----------------+-----------------------------+----------------
both( . x4o .    ) |   4 |   4   0   0   0 | 144   *   *   *   *   *   * |  1  0  0  1   0
      β3x . .      ♦   6 |   3   0   3   0 |   * 192   *   *   *   *   * |  1  1  0  0   0
      . . o3β      ♦   3 |   0   0   0   3 |   *   * 192   *   *   *   * |  0  0  1  1   0
sefa( β3x4o .    ) |   4 |   0   0   4   0 |   *   *   * 144   *   *   * |  1  0  0  0   1
sefa( β3x . β2*a ) |   4 |   1   2   1   0 |   *   *   *   * 576   *   * |  0  1  0  0   1
sefa( β . o3β2*a ) |   3 |   0   2   0   1 |   *   *   *   *   * 576   * |  0  0  1  0   1
sefa( . x4o3β    ) |   8 |   4   0   0   4 |   *   *   *   *   *   * 144 |  0  0  0  1   1
-------------------+-----+-----------------+-----------------------------+----------------
      β3x4o .      ♦  24 |  24   0  24   0 |   6   8   0   6   0   0   0 | 24  *  *  *   *
      β3x . β2*a   ♦  12 |   6   6   6   0 |   0   2   0   0   6   0   0 |  * 96  *  *   *
      β . o3β2*a   ♦   6 |   0   6   0   6 |   0   0   2   0   0   6   0 |  *  * 96  *   *
      . x4o3β      ♦  24 |  24   0   0  24 |   6   0   8   0   0   0   6 |  *  *  * 24   *
sefa( β3x4o3β    ) ♦  12 |   4   8   4   4 |   0   0   0   1   4   4   1 |  *  *  *  * 144

starting figure: x3x4o3x