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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 sirco as a pre-image these intersection points might differ on its 2 edge types. Therefore sirco 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 polyhedron. That one here is scaled such so that the shorter one becomes unity. Then the larger edge will have size q = sqrt(2).

The u-edges of each layer here become pseudo edges only. In fact, those are the diagonals of the tegum summed faces on the rhombohedral positions.

Incidence matrix according to Dynkin symbol

uo3qx4ou&#zq   → height = 0
(q-laced tegum sum of (u,q)-toe and (x,u)-tic)

o.3o.4o.     | 24  * |  2  2  0 | 1  1  2 0
.o3.o4.o     |  * 24 |  0  2  2 | 0  1  2 1
-------------+-------+----------+----------
.. q. ..     |  2  0 | 24  *  * | 1  0  1 0  q
oo3oo4oo&#q  |  1  1 |  * 48  * | 0  1  1 0  q
.. .x ..     |  0  2 |  *  * 24 | 0  0  1 1  x
-------------+-------+----------+----------
.. q.4o.     |  4  0 |  4  0  0 | 6  *  * *  q-{4}
uo .. ou&#zq |  2  2 |  0  4  0 | * 12  * *  q-{4}
.. qx ..&#q  |  2  2 |  1  2  1 | *  * 24 *  {(xqqq)}
.o3.x ..     |  0  3 |  0  0  3 | *  *  * 8  x-{3}