Acronym  rebtatoh 
Name  rectified bitruncated tetrahedraloctahedral honeycomb 
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 batatoh all edges belong to a single orbit of symmetry, i.e. rectification clearly is applicable, without any recourse to Conway's ambification (chosing the former edge centers generally). None the less, wrt. the individual cells of the preimage, there an ambification is possible only, i.e. tut cannot be rectified (within this stronger sense).
Still, because the preimage uses different polygonal faces, this would result in 2 different edge sizes in the outcome polychoron. That one here is scaled such so that the shorter one becomes unity. Then the larger edge will have size h = sqrt(3) = 1.732051.
Incidence matrix according to Dynkin symbol
xo3od3do3ox3*a&#zh (N → ∞) → height = 0, d = 3x (pseudo) (hlaced tegum sum of 2 inverted (x,d)richs) o.3o.3o.3o.3*a &  6N  4 4  2 2 6 2  1 3 2 ++++ x. .. .. .. &  2  12N *  1 1 1 0  1 1 1 x oo3oo3oo3oo3*a&#h  2  * 12N  0 0 2 1  0 2 1 h ++++ x.3o. .. .. &  3  3 0  4N * * *  1 1 0 x. .. .. o.3*a &  3  3 0  * 4N * *  1 0 1 xo .. .. .. &#h &  3  1 2  * * 12N *  0 1 1 .. od3do .. &#zh  6  0 6  * * * 2N  0 2 0 h3h ++++ x.3o. .. o.3*a & ♦ 6  12 0  4 4 0 0  N * * xo3od3do .. &#zh & ♦ 18  12 24  4 0 12 4  * N * xo .. .. ox3*a&#h ♦ 6  6 6  0 2 6 0  * * 2N
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