Rectification wrt. a non-regular polytope is meant to be the singular instance of truncations on all vertices at such a depth that the hyperplane intersections on the former edges will coincide (provided such a choice exists). Within the specific case of sidpith as a pre-image these intersection points might differ on its 2 edge types. Therefore sidpith cannot be rectified (within this stronger sense). Nonetheless the Conway operator of ambification (chosing the former edge centers generally) clearly is applicable. This would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the smaller one becomes unity. Then the longer edge will have size q = sqrt(2).

All u = 2 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.

Incidence matrix according to Dynkin symbol

((uo3ox3qo4ou))&#zq   → height = 0
(q-laced tegum sum of (u,q)-rico and (x,u)-srit)

  o.3o.3o.4o.       | 96  * |   4   4   0 |  2  2  2   2   4  0  0 | 1  1  2  2  0
  .o3.o3.o4.o       |  * 96 |   0   4   4 |  0  0  2   4   2  2  2 | 0  2  1  2  1
--------------------+-------+-------------+------------------------+--------------
  .. .. q. ..       |  2  0 | 192   *   * |  1  1  0   0   1  0  0 | 1  0  1  1  0
  oo3oo3oo4oo  &#q  |  1  1 |   * 384   * |  0  0  1   1   1  0  0 | 0  1  1  1  0
  .. .x .. ..       |  0  2 |   *   * 192 |  0  0  0   1   0  1  1 | 0  1  0  1  1
--------------------+-------+-------------+------------------------+--------------
  .. o.3q. ..       |  3  0 |   3   0   0 | 64  *  *   *   *  *  * | 1  0  0  1  0
  .. .. q.4o.       |  4  0 |   4   0   0 |  * 48  *   *   *  *  * | 1  0  1  0  0
((uo .. .. ou))&#zq |  2  2 |   0   4   0 |  *  * 96   *   *  *  * | 0  1  1  0  0  q-{4}
  .. ox .. ..  &#q  |  1  2 |   0   2   1 |  *  *  * 192   *  *  * | 0  1  0  1  0  isot
  .. .. qo ..  &#q  |  2  1 |   1   2   0 |  *  *  *   * 192  *  * | 0  0  1  1  0  q-{3}
  .o3.x .. ..       |  0  3 |   0   0   3 |  *  *  *   *   * 64  * | 0  1  0  0  1
  .. .x3.o ..       |  0  3 |   0   0   3 |  *  *  *   *   *  * 64 | 0  0  0  1  1
--------------------+-------+-------------+------------------------+--------------
  .. o.3q.4o.       | 12  0 |  24   0   0 |  8  6  0   0   0  0  0 | 8  *  *  *  *  q-co
((uo3ox .. ou))&#zq |  3  6 |   0  12   6 |  0  0  3   6   0  2  0 | * 32  *  *  *  retrip
((uo .. qo4ou))&#zq |  8  4 |   8  16   0 |  0  2  4   0   8  0  0 | *  * 24  *  *  q-co
  .. ox3qo ..  &#q  |  3  3 |   3   6   3 |  1  0  0   3   3  0  1 | *  *  * 64  *  verf(sidpith)
  .o3.x3.o ..       |  0  6 |   0   0  12 |  0  0  0   0   0  4  4 | *  *  *  * 16  x-oct