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 xhi as a pre-image these intersection points might differ on its 2 edge types. Therefore xhi 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 polychoron. That one here is scaled such so that the smaller one becomes unity. Then the medium edge will have size f = (1+sqrt(5))/2 and the longer one has size h = sqrt(3).

All d = 3 edges, used in the below descriptions, only qualify as pseudo edges wrt. the full polychoron.

Incidence matrix according to Dynkin symbol

((xo3od3do5of))&#zh
(h-laced tegum sum of (x,d)-srix and (d,f)-srahi)

  o.3o.3o.5o.       | 3600    * |    2     4    0 |    1    4    2    2   0 |   2    2   1
  .o3.o3.o5.o       |    * 3600 |    0     4    2 |    0    2    2    4   1 |   1    2   2
--------------------+-----------+-----------------+-------------------------+-------------
  x. .. .. ..       |    2    0 | 3600     *    * |    1    2    0    0   0 |   2    1   0  x
  oo3oo3oo5oo  &#h  |    1    1 |    * 14400    * |    0    1    1    1   0 |   1    1   1  h
  .. .. .. .f       |    0    2 |    *     * 3600 |    0    0    0    2   1 |   0    1   2  f
--------------------+-----------+-----------------+-------------------------+-------------
  x.3o. .. ..       |    3    0 |    3     0    0 | 1200    *    *    *   * |   2    0   0  x-{3}
  xo .. .. ..  &#h  |    2    1 |    1     2    0 |    * 7200    *    *   * |   1    1   0  {(xhh)}
((.. od3do ..))&#zh |    3    3 |    0     6    0 |    *    * 2400    *   * |   1    0   1  h-{6}
  .. .. .. of  &#h  |    1    2 |    0     2    1 |    *    *    * 7200   * |   0    1   1  {(fhh)}
  .. .. .o5.f       |    0    5 |    0     0    5 |    *    *    *    * 720 |   0    0   2  f-{5}
--------------------+-----------+-----------------+-------------------------+-------------
((xo3od3do ..))&#zh |   12    6 |   12    24    0 |    4   12    4    0   0 | 600    *   *  retut
  xo .. .. of  &#h  |    2    2 |    1     4    1 |    0    2    0    2   0 |   * 3600   *  2-ap variant
((.. od3do5of))&#zh |   30   60 |    0   120   60 |    0    0   20   60  12 |   *    * 120  reti