Acronym  retrip (alt.: amtrip) 
Name 
rectified/ambiated trip, kernel of trip and m m3o, o2o3o symmetric co relative 
Circumradius  sqrt(2/3) = 0.816497 
Confer 

Rectification wrt. a nonregular 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 trip as a preimage these intersection points might differ on its 2 edge types. Therefore trip 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 larger one becomes unity. Then the shorter edge will have size c = q/2 = 1/sqrt(2).
The 6 nonpolar triangles {(t,T,T)} have vertex angles t = arccos(3/4) = 41.409622° resp. T = arccos[1/sqrt(8)] = 69.295189°.
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 ouo3xox&#qt = ou uo3ox&#zq, but then the circumradius and given heights too had to be rescaled accordingly for sure. Thereby the uedges then would qualify as those pseudo edges.
Incidence matrix according to Dynkin symbol
oqo3coc&#xt → both heights = c = q/2 = 1/sqrt(2) = 0.707107 o..3o..  3 * *  2 2 0 0  1 2 1 0 0 .o.3.o.  * 3 *  0 2 2 0  0 1 2 1 0 ..o3..o  * * 3  0 0 2 2  0 0 1 2 1 +++ ... c..  2 0 0  3 * * *  1 1 0 0 0 c oo.3oo.&#x  1 1 0  * 6 * *  0 1 1 0 0 x .oo3.oo&#x  0 1 1  * * 6 *  0 0 1 1 0 x ... ..c  0 0 2  * * * 3  0 0 0 1 1 c +++ o..3c..  3 0 0  3 0 0 0  1 * * * * c{3} ... co.&#x  2 1 0  1 2 0 0  * 3 * * * {(t,T,T)} oqo ...&#xt  1 2 1  0 2 2 0  * * 3 * * {4} ... .oc&#x  0 1 2  0 0 2 1  * * * 3 * {(t,T,T)} ..o3..c  0 0 3  0 0 0 3  * * * * 1 c{3}
or o..3o.. &  6 *  2 2  1 2 1 .o.3.o.  * 3  0 4  0 2 2 +++ ... c.. &  2 0  6 *  1 1 0 c oo.3oo.&#x &  1 1  * 12  0 1 1 x +++ o..3c.. &  3 0  3 0  2 * * c{3} ... co.&#x &  2 1  1 2  * 6 * {(t,T,T)} oqo ...&#xt  2 2  0 4  * * 3 {4}
oq qo3oc&#zx → height = 0, c = q/2 = 1/sqrt(2) = 0.707107 (tegum sum of q{3} and gyrated (q,c)trip) o. o.3o.  3 *  4 0  2 2 0 .o .o3.o  * 6  2 2  1 2 1 +++ oo oo3oo&#x  1 1  12 *  1 1 0 x .. .. .c  0 2  * 6  0 1 1 c +++ oq qo ..&#zx  2 2  4 0  3 * * {4} .. .. oc&#x  1 2  2 1  * 6 * {(t,T,T)} .. .o3.c  0 3  0 3  * * 2 c{3}
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