Truncation wrt. a non-regular polytope is meant to any instance of truncations on all vertices. For pre-images with different edge types however the ratio correlation of the remaining bits of those becomes arbitrary. Therefore toe cannot be truncated (within this stronger sense). Nonetheless the Conway operator of ambification (chosing the edge centers generally) clearly is applicable. And thus an expansion of that ambification could replace the usual expansion of the rectification here. This would result in 3 different edge sizes in the outcome polyhedron. That one here is scaled such so that the shorter specified one becomes unity. Then the larger specified edge will have size b=sqrt(3/2). The third one would be the arbitrary expansion size y (corresponding to the arbitrary truncation depth). In fact, for y=0 this results again in retoe, while y → ∞ results again in the pre-image toe (rescaled back down accordingly).

Incidence matrix according to Dynkin symbol

xo4ya3ay&#zb   → height = 0
                 y > 0 (arbitrary expansion size)
                 a = y + 3/sqrt(2) (pseudo)
                 b = sqrt(3/2) = 1.224745
(b-laced tegum sum of x4y3a and o4a3y)

o.4o.3o.     | 48  * |  1  1  1  0 | 1  1 1
.o4.o3.o     |  * 24 |  0  0  2  1 | 0  1 2
-------------+-------+-------------+-------
x. .. ..     |  2  0 | 24  *  *  * | 1  1 0  x
.. y. ..     |  2  0 |  * 24  *  * | 1  0 1  y
oo4oo3oo&#b  |  1  1 |  *  * 48  * | 0  1 1  b
.. .. .y     |  0  2 |  *  *  * 12 | 0  0 2  y
-------------+-------+-------------+-------
x.4y. ..     |  8  0 |  4  4  0  0 | 6  * *  ditetragon x4y
xo .. ..&#b  |  2  1 |  1  0  2  0 | * 24 *  isot ox&#b
.. ya3ay&#zb |  6  6 |  0  3  6  3 | *  * 8  dihexagon y6b