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 tratet as a pre-image these intersection points might differ on its 2 edge types. Therefore tratet 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).

The non-polar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.

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

Incidence matrix according to Dynkin symbol

uo3ox3oo xo3ou&#zq   → height = 0

o.3o.3o. o.3o.     | 12  * |  2  6  0 | 1  3  6  6  0  0 |  3 3  2  6 0 | 1 3  2
.o3.o3.o .o3.o     |  * 18 |  0  4  4 | 0  2  8  2  2  2 |  4 1  4  4 1 | 2 2  2
-------------------+-------+----------+------------------+--------------+-------
.. .. .. x. ..     |  2  0 | 12  *  * | 1  0  0  3  0  0 |  0 3  0  3 0 | 0 3  1
oo3oo3oo oo3oo&#q  |  1  1 |  * 72  * | 0  1  2  1  0  0 |  2 1  1  2 0 | 1 2  1
.. .x .. .. ..     |  0  2 |  *  * 36 | 0  0  2  0  1  1 |  2 0  2  1 1 | 2 1  1
-------------------+-------+----------+------------------+--------------+-------
.. .. .. x.3o.     |  3  0 |  3  0  0 | 4  *  *  *  *  * |  0 3  0  0 0 | 0 3  0
uo .. .. .. ou&#zq |  2  2 |  0  4  0 | * 18  *  *  *  * |  2 1  0  0 0 | 1 2  0
.. ox .. .. ..&#q  |  1  2 |  0  2  1 | *  * 72  *  *  * |  1 0  1  1 0 | 1 1  1
.. .. .. xo ..&#q  |  2  1 |  1  2  0 | *  *  * 36  *  * |  0 1  0  2 0 | 0 2  1
.o3.x .. .. ..     |  0  3 |  0  0  3 | *  *  *  * 12  * |  2 0  0  0 1 | 2 1  0
.. .x3.o .. ..     |  0  3 |  0  0  3 | *  *  *  *  * 12 |  0 0  2  0 1 | 2 0  1
-------------------+-------+----------+------------------+--------------+-------
uo3ox .. .. ou&#zq ♦  3  6 |  0 12  6 | 0  3  6  0  2  0 | 12 *  *  * * | 1 1  0
uo .. .. xo3ou&#zq ♦  6  3 |  6 12  0 | 2  3  0  6  0  0 |  * 6  *  * * | 0 2  0
.. ox3oo .. ..&#q  ♦  1  3 |  0  3  3 | 0  0  3  0  0  1 |  * * 24  * * | 1 0  1
.. ox .. xo ..&#q  ♦  2  2 |  1  4  1 | 0  0  2  2  0  0 |  * *  * 36 * | 0 1  1
.o3.x3.o .. ..     ♦  0  6 |  0  0 12 | 0  0  0  0  4  4 |  * *  *  * 3 | 2 0  0
-------------------+-------+----------+------------------+--------------+-------
uo3ox3oo .. ou&#zq ♦  4 12 |  0 24 24 | 0  6 24  0  8  8 |  4 0  8  0 2 | 3 *  *
uo3ox .. xo3ou&#zq ♦  9  9 |  9 36  9 | 3  9 18 18  3  0 |  3 3  0  9 0 | * 4  *
.. ox3oo xo ..&#q  ♦  2  3 |  1  6  3 | 0  0  6  3  0  1 |  0 0  2  3 0 | * * 12