Acronym ...
Name rectified Shephard's hexadecachoron,
complex polychoron op-4-o2-3-x2-3-o2
Coordinates (εpn, εpm, 0, 0)   & all permutations, each for any 1≤n,m≤p, where εp=exp(2πi/p)
Face vector 6p2, 12p3, 4p3(p+1), p(p3+4)
Confer
general polytopal classes:
complex polytopes  

This is the rectification of Shephard's generalised hexadecachoron. Accordingly it re-uses the edge count of its pre-image as its new vertex count. The new edge type will be 2-fold, i.e. are real ones only. It will have 2 complex face types, the first being the duals of the ones of its pre-image (which here are real space triangles), the others are the faces of the former's vertex figure (real space triangles again). There are 2 complex cell types too, the first being Shephard's generalised octahedras, the others are the former's vertex figures, i.e. (real space) octs. The new vertex figures in here are the complex reducible polyhedra x2   x2-4-op.


Incidence matrix according to Dynkin symbol

op-4-o2-3-x2-3-o2

.    .    .    .  | 6p2 ♦  4p  | 2p2 2p  |  2 p2 
-----------------+-----+------+---------+------
.    .    x2   .  |  2  | 12p3 |  p   1  |  1 p 
-----------------+-----+------+---------+------
.    o2-3-x2   .  |  3  |   3  | 4p4  *  |  1 1 
.    .    x2-3-o2 |  3  |   3  |  *  4p3 |  0 p 
-----------------+-----+------+---------+------
op-4-o2-3-x2   .  ♦ 3p  |  3p2 |  p3  0  | 4p * 
.    o2-3-x2-3-o2 ♦  6  |  12  |  4   4  |  * p4

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