This hypercompact hyperbolic tesselation uses hihexat in the sense of an infinite bollohedron and squat in the sense of an infinite horohedron as cells.

This hemiation indeed becomes scaliform, because all edges by mere alternation already do have the same size: diagonals of either of the former squares. I.e. no afterwards edge resizements are required (except of a homogenuous global scaling). However, because of the introduction of the former vertex figure as a further cell, which here just is a Johnson solid, it cannot become uniform.

Incidence matrix according to Dynkin symbol

s4o3o4s4*b

demi( . . . .    ) | 4NMK |    3     6    3    3 |    3    12     9    6 |   1   3    3   1    9
-------------------+------+----------------------+-----------------------+----------------------
      s4o . .      |    2 | 6NMK     *    *    * |    2     2     0    0 |   1   1    0   0    2
      s 2 . s      |    2 |    * 12NMK    *    * |    0     2     2    0 |   0   1    1   0    2
      . o . s4*b   |    2 |    *     * 6NMK    * |    0     2     0    2 |   0   1    0   1    2
      . . o4s      |    2 |    *     *    * 6NMK |    0     0     2    2 |   0   0    1   1    2
-------------------+------+----------------------+-----------------------+----------------------
sefa( s4o3o .    ) |    3 |    3     0    0    0 | 4NMK     *     *    * |   1   0    0   0    1
sefa( s4o . s4*b ) |    4 |    1     2    1    0 |    * 12NMK     *    * |   0   1    0   0    1
sefa( s 2 o4s    ) |    3 |    0     2    0    1 |    *     * 12NMK    * |   0   0    1   0    1
sefa( . o3o4s4*b ) |    6 |    0     0    3    3 |    *     *     * 4NMK |   0   0    0   1    1
-------------------+------+----------------------+-----------------------+----------------------
      s4o3o .      ♦    4 |    6     0    0    0 |    4     0     0    0 | NMK   *    *   *    *
      s4o . s4*b   ♦   2M |    M    2M    M    0 |    0    2M     0    0 |   * 6NK    *   *    *
      s 2 o4s      ♦    4 |    0     4    0    2 |    0     0     4    0 |   *   * 3NMK   *    *
      . o3o4s4*b   ♦   2K |    0     0   3K   3K |    0     0     0   2K |   *   *    * 2NM    *
sefa( s4o3o4s4*b ) ♦    9 |    3     6    3    3 |    1     3     3    1 |   *   *    *   * 4NMK

starting figure: x4o3o4x4*b