Acronym	...
Name	rectified/ambified n/d-prism, o o-n/d-o symmetric co relative
	©
Circumradius	1/[sqrt(2) sin(π d/n)]
Face vector	3n, 6n, 3n+2
Especially	retrip (n/d=3)   co (n/d=4)   repip (n/d=5)
Confer	ambification pre-image: n/d-p
External links

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 n/d-p as a pre-image these intersection points might differ on its 2 edge types. Therefore n/d-p in generally 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 square sides become unity. Then the shorter edge will have size c = x(n/d)/x(4) = sqrt(2) cos(π d/n).

All q = sqrt(2) edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polyhedron.

Note that the below description also could be scaled by q into a further convenient form ouo-n/d-yoy&#qt = ou uo-n/d-oy&#zq, where for abbreviation y = x(n/d), but then the circumradius and given heights too had to be rescaled accordingly for sure. Thereby the u-edges then would qualify as those pseudo edges.

Incidence matrix according to Dynkin symbol

oqo-n/d-coc&#xt   → both heights = 1/sqrt(2) = 0.707107
                    c = x(n/d)/x(4) = sqrt(2) cos(π d/n)

o..-n/d-o..     | n * * | 2  2  0 0 | 1 2 1 0 0
.o.-n/d-.o.     | * n * | 0  2  2 0 | 0 1 2 1 0
..o-n/d-..o     | * * n | 0  0  2 2 | 0 0 1 2 1
----------------+-------+-----------+----------
...     c..     | 2 0 0 | n  *  * * | 1 1 0 0 0  c
oo.-n/d-oo.&#x  | 1 1 0 | * 2n  * * | 0 1 1 0 0  x
.oo-n/d-.oo&#x  | 0 1 1 | *  * 2n * | 0 0 1 1 0  x
...     ..c     | 0 0 2 | *  *  * n | 0 0 0 1 1  c
----------------+-------+-----------+----------
o..-n/d-c..     | n 0 0 | n  0  0 0 | 1 * * * *  c-{n/d}
...     co.&#x  | 2 1 0 | 1  2  0 0 | * n * * *
oqo     ...&#xt | 1 2 1 | 0  2  2 0 | * * n * *  {4}
...     .oc&#x  | 0 1 2 | 0  0  2 1 | * * * n *
..o-n/d-..c     | 0 0 n | 0  0  0 n | * * * * 1  c-{n/d}

or
o..-n/d-o..     & | 2n * |  2  2 | 1  2 1
.o.-n/d-.o.       |  * n |  0  4 | 0  2 2
------------------+------+-------+-------
...     c..     & |  2 0 | 2n  * | 1  1 0  c
oo.-n/d-oo.&#x  & |  1 1 |  * 4n | 0  1 1  x
------------------+------+-------+-------
o..-n/d-c..     & |  n 0 |  3  0 | 2  * *  c-{n/d}
...     co.&#x  & |  2 1 |  1  2 | * 2n *
oqo     ...&#xt   |  2 2 |  0  4 | *  * n  {4}

oq qo-n/d-oc&#zx   → height = 0, c = x(n/d)/x(4) = sqrt(2) cos(π d/n)
(tegum sum of q-{n/d} and gyrated (q,c)-n/d-p)

o. o.-n/d-o.     | n  * |  4  0 | 2  2 0
.o .o-n/d-.o     | * 2n |  2  2 | 1  2 1
-----------------+------+-------+-------
oo oo-n/d-oo&#x  | 1  1 | 4n  * | 1  1 0  x
.. ..     .c     | 0  2 |  * 2n | 0  1 1  c
-----------------+------+-------+-------
oq qo     ..&#zx | 2  2 |  4  0 | n  * *  {4}
.. ..     oc&#x  | 1  2 |  2  1 | * 2n *
.. .o-n/d-.c     | 0  3 |  0  3 | *  * 2  c-{n/d}