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 tah as a pre-image these intersection points might differ on its 2 edge types. Therefore tah 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 medium edge will have size q = sqrt(2) and the longer one has size h = sqrt(3).

All d = 3 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.

Incidence matrix according to Dynkin symbol

xo3od3do4oq&#zh
(h-laced tegum sum of (x,d)-rico and (d,q)-srit)

o.3o.3o.4o.     | 96  * |  2   4  0 |  1   4  2   2  0 |  2  2 1
.o3.o3.o4.o     |  * 96 |  0   4  2 |  0   2  2   4  1 |  1  2 2
----------------+-------+-----------+------------------+--------
x. .. .. ..     |  2  0 | 96   *  * |  1   2  0   0  0 |  2  1 0  x
oo3oo3oo4oo&#h  |  1  1 |  * 384  * |  0   1  1   1  0 |  1  1 1  h
.. .. .. .q     |  0  2 |  *   * 96 |  0   0  0   2  1 |  0  1 2  q
----------------+-------+-----------+------------------+--------
x.3o. .. ..     |  3  0 |  3   0  0 | 32   *  *   *  * |  2  0 0  x-{3}
xo .. .. ..&#h  |  2  1 |  1   2  0 |  * 192  *   *  * |  1  1 0  {(xhh)}
.. od3do ..&#zh |  3  3 |  0   6  0 |  *   * 64   *  * |  1  0 1  h-{6}
.. .. .. oq&#h  |  1  2 |  0   2  1 |  *   *  * 192  * |  0  1 1  {(qhh)}
.. .. .o4.q     |  0  4 |  0   0  4 |  *   *  *   * 24 |  0  0 2  q-{4}
----------------+-------+-----------+------------------+--------
xo3od3do ..&#zh | 12  6 | 12  24  0 |  4  12  4   0  0 | 16  * *  retut
xo .. .. oq&#h  |  2  2 |  1   4  1 |  0   2  0   2  0 |  * 96 *  2-ap variant
.. od3do4oq&#zh | 12 24 |  0  48 24 |  0   0  8  24  6 |  *  * 8  retoe