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

uo3ox3oo3oo ou&#zq   → height = 0

o.3o.3o.3o. o.     | 5  * |  8  0 |  4 12  0  0 |  6  8  0  0 | 4  2 0
.o3.o3.o3.o .o     | * 20 |  2  6 |  1  6  3  6 |  3  6  3  2 | 3  2 1
-------------------+------+-------+-------------+-------------+-------
oo3oo3oo3oo oo&#q  | 1  1 | 40  * |  1  3  0  0 |  3  3  0  0 | 3  1 0
.. .x .. .. ..     | 0  2 |  * 60 |  0  1  1  2 |  1  2  2  1 | 2  1 1
-------------------+------+-------+-------------+-------------+-------
uo .. .. .. ou&#zq | 2  2 |  4  0 | 10  *  *  * |  3  0  0  0 | 3  0 0  q-{4}
.. ox .. .. ..&#q  | 1  2 |  2  1 |  * 60  *  * |  1  2  0  0 | 2  1 0  {(t,T,T)}
.o3.x .. .. ..     | 0  3 |  0  3 |  *  * 20  * |  1  0  2  0 | 2  0 1
.. .x3.o .. ..     | 0  3 |  0  3 |  *  *  * 40 |  0  1  1  1 | 1  1 1
-------------------+------+-------+-------------+-------------+-------
uo3ox .. .. ou&#zq ♦ 3  6 | 12  6 |  3  6  2  0 | 10  *  *  * | 2  0 0
.. ox3oo .. ..&#q  ♦ 1  3 |  3  3 |  0  3  0  1 |  * 40  *  * | 1  1 0
.o3.x3.o .. ..     ♦ 0  6 |  0 12 |  0  0  4  4 |  *  * 10  * | 1  0 1
.. .x3.o3.o ..     ♦ 0  4 |  0  6 |  0  0  0  4 |  *  *  * 10 | 0  1 1
-------------------+------+-------+-------------+-------------+-------
uo3ox3oo .. ou&#zq ♦ 4 12 | 24 24 |  6 24  8  8 |  4  8  2  0 | 5  * *
.. ox3oo3oo ..&#q  ♦ 1  4 |  4  6 |  0  6  0  4 |  0  4  0  1 | * 10 *
.o3.x3.o3.o ..     ♦ 0 10 |  0 30 |  0  0 10 20 |  0  0  5  5 | *  * 2

ouo3xox3ooo3ooo&#qt   → both heights = 1

o..3o..3o..3o..     | 10 *  * |  6  2  0  0 |  3  6  1  6  0  0  0 | 3 2  3  6  0 0 0 | 1 3 2 0 0
.o.3.o.3.o.3.o.     |  * 5  * |  0  4  4  0 |  0  0  4  6  6  0  0 | 0 0  6  4  4 0 0 | 0 4 1 1 0
..o3..o3..o3..o     |  * * 10 |  0  0  2  6 |  0  0  1  0  6  3  6 | 0 0  3  0  6 3 2 | 0 3 0 2 1
--------------------+---------+-------------+----------------------+------------------+----------
... x.. ... ...     |  2 0  0 | 30  *  *  * |  1  2  0  1  0  0  0 | 2 1  1  2  0 0 0 | 1 2 1 0 0
oo.3oo.3oo.3oo.&#q  |  1 1  0 |  * 20  *  * |  0  0  1  3  0  0  0 | 0 0  3  3  0 0 0 | 0 3 1 0 0
.oo3.oo3.oo3.oo&#q  |  0 1  1 |  *  * 20  * |  0  0  1  0  3  0  0 | 0 0  3  0  3 0 0 | 0 3 0 1 0
... ..x ... ...     |  0 0  2 |  *  *  * 30 |  0  0  0  0  1  1  2 | 0 0  1  0  2 2 1 | 0 2 0 1 1
--------------------+---------+-------------+----------------------+------------------+----------
o..3x.. ... ...     |  3 0  0 |  3  0  0  0 | 10  *  *  *  *  *  * | 2 0  1  0  0 0 0 | 1 2 0 0 0
... x..3o.. ...     |  3 0  0 |  3  0  0  0 |  * 20  *  *  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0 0
ouo ... ... ...&#qt |  1 2  1 |  0  2  2  0 |  *  * 10  *  *  *  * | 0 0  3  0  0 0 0 | 0 3 0 0 0  q-{4}
... xo. ... ...&#q  |  2 1  0 |  1  2  0  0 |  *  *  * 30  *  *  * | 0 0  1  2  0 0 0 | 0 2 1 0 0  {(t,T,T)}
... .ox ... ...&#q  |  0 1  2 |  0  0  2  1 |  *  *  *  * 30  *  * | 0 0  1  0  2 0 0 | 0 2 0 1 0  {(t,T,T)}
..o3..x ... ...     |  0 0  3 |  0  0  0  3 |  *  *  *  *  * 10  * | 0 0  1  0  0 2 0 | 0 2 0 0 1
... ..x3..o ...     |  0 0  3 |  0  0  0  3 |  *  *  *  *  *  * 20 | 0 0  0  0  1 1 1 | 0 1 0 1 1
--------------------+---------+-------------+----------------------+------------------+----------
o..3x..3o.. ...     ♦  6 0  0 | 12  0  0  0 |  4  4  0  0  0  0  0 | 5 *  *  *  * * * | 1 1 0 0 0
... x..3o..3o..     ♦  4 0  0 |  6  0  0  0 |  0  4  0  0  0  0  0 | * 5  *  *  * * * | 1 0 1 0 0
ouo3xox ... ...&#qt ♦  3 3  3 |  3  6  6  3 |  1  0  3  3  3  1  0 | * * 10  *  * * * | 0 2 0 0 0
... xo.3oo. ...&#q  ♦  3 1  0 |  3  3  0  0 |  0  1  0  3  0  0  0 | * *  * 20  * * * | 0 1 1 0 0
... .ox3.oo ...&#q  ♦  0 1  3 |  0  0  3  3 |  0  0  0  0  3  0  1 | * *  *  * 20 * * | 0 1 0 1 0
..o3..x3..o ...     ♦  0 0  6 |  0  0  0 12 |  0  0  0  0  0  4  4 | * *  *  *  * 5 * | 0 1 0 0 1
... ..x3..o3..o     ♦  0 0  4 |  0  0  0  6 |  0  0  0  0  0  0  4 | * *  *  *  * * 5 | 0 0 0 1 1
--------------------+---------+-------------+----------------------+------------------+----------
o..3x..3o..3o..     ♦ 10 0  0 | 30  0  0  0 | 10 20  0  0  0  0  0 | 5 5  0  0  0 0 0 | 1 * * * *
ouo3xox3ooo ...&#qt ♦  6 4  6 | 12 12 12 12 |  4  4  6 12 12  4  4 | 1 0  4  4  4 1 0 | * 5 * * *
... xo.3oo.3oo.&#q  ♦  4 1  0 |  6  4  0  0 |  0  4  0  6  0  0  0 | 0 1  0  4  0 0 0 | * * 5 * *
... .ox3.oo3.oo&#q  ♦  0 1  4 |  0  0  4  6 |  0  0  0  0  6  0  4 | 0 0  0  0  4 0 1 | * * * 5 *
..o3..x3..o3..o     ♦  0 0 10 |  0  0  0 30 |  0  0  0  0  0 10 20 | 0 0  0  0  0 5 5 | * * * * 1