Acronym	tacytatoh (old: tabtatoh)
Name	truncated cyclotruncated tetrahedral-octahedral honeycomb (truncated bitruncated tetrahedral-octahedral honeycomb)
Confer	extremal cases: cytatoh   recytatoh   general polytopal classes: isogonal
External links

Truncation would result in 3 different edge sizes in the outcome isohedral polychoron. That one here is scaled such so that the shorter specified one becomes unity. Then the larger specified edge will have size h=sqrt(3). The third one would be the arbitrary expansion size y (wrt. the rectified extremum, i.e. corresponding to the arbitrary truncation depth). In fact, for y=0 this results again in recytatoh, while y → ∞ results again in the pre-image cytatoh (rescaled back down accordingly).

Incidence matrix according to Dynkin symbol

xo3yb3by3ox3*a&#zh   (N → ∞)   → height = 0,
                                 y > 0 (depending on truncation depth),
                                 b = y+3 (pseudo)
(h-laced tegum sum of 2 inverted (x,y,b)-tatohs)

o.3o.3o.3o.3*a       | 12N |   2  1   2 |  2  1   3  2 | 1 3  2
---------------------+-----+------------+--------------+-------
x. .. .. ..        & |   2 | 12N  *   * |  1  1   1  0 | 1 1  1  x
.. y. .. ..        & |   2 |   * 6N   * |  2  0   0  2 | 1 3  0  y
oo3oo3oo3oo3*a&#h    |   2 |   *  * 12N |  0  0   2  1 | 0 2  1  h
---------------------+-----+------------+--------------+-------
x.3y. .. ..        & |   6 |   3  3   0 | 4N  *   *  * | 1 1  0
x. .. .. o.3*a     & |   3 |   3  0   0 |  * 4N   *  * | 1 0  1
xo .. .. ..   &#h  & |   3 |   1  0   2 |  *  * 12N  * | 0 1  1
.. yb3by ..   &#zh   |  12 |   0  6   6 |  *  *   * 2N | 0 2  0  y6h
---------------------+-----+------------+--------------+-------
x.3y. .. o.3*a     & ♦  12 |  12  6   0 |  4  4   0  0 | N *  *
xo3yb3by ..   &#zh & ♦  36 |  12 18  24 |  4  0  12  4 | * N  *
xo .. .. ox3*a&#h    ♦   6 |   6  0   6 |  0  2   6  0 | * * 2N