Acronym	repip (alt. ampip)
Name	rectified/ambified pip, o2o5o symmetric co relative
	©
Circumradius	sqrt[1+1/sqrt(5)] = 1.203002
Face vector	15, 30, 17
Confer	more general: oqo-n/d-coc&#xt   ambification pre-image: pip
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 pip as a pre-image these intersection points might differ on its 2 edge types. Therefore pip 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 smaller one becomes unity. Then the longer edge will have size c = f/q.

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

Incidence matrix according to Dynkin symbol

oqo5coc&#xt   → both heights = 1/sqrt(2) = 0.707107, c = f/q = (1+sqrt(5))/sqrt(8) = 1.144123

o..5o..     & | 10 * |  2  2 | 1  2 1
.o.5.o.       |  * 5 |  0  4 | 0  2 2
--------------+------+-------+-------
... c..     & |  2 0 | 10  * | 1  1 0
oo.5oo.&#x  & |  1 1 |  * 20 | 0  1 1
--------------+------+-------+-------
o..5c..     & |  5 0 |  5  0 | 2  * *
... co.&#x  & |  2 1 |  1  2 | * 10 *
oqo ...&#xt   |  2 2 |  0  4 | *  * 5

oq qo5oc&#zx   → height = 0, c = f/q = (1+sqrt(5))/sqrt(8) = 1.144123
(tegum sum of q-{5} and gyrated (q,c)-pip)

o. o.5o.     | 5  * |  4  0 | 2  2 0
.o .o5.o     | * 10 |  2  2 | 1  2 1
-------------+------+-------+-------
oo oo5oo&#x  | 1  1 | 20  * | 1  1 0
.. .. .c     | 0  2 |  * 10 | 0  1 1
-------------+------+-------+-------
oq qo ..&#zx | 2  2 |  4  0 | 5  * *
.. .. oc&#x  | 1  2 |  2  1 | * 10 *
.. .o5.c     | 0  5 |  0  5 | *  * 2