The truncation generally keeps the edges of the regular pre-image, but pulls them somehow apart, then filling in the former vertex figures. Here it becomes applied to Shephard's 3-generalised octahedron, i.e. x₂-3-o₂-4-o₃. Thus the new vertex count derives as the product of the former vertex count with the vertex count of the former vertex figure. For new edges one gets both, those of the regular and of its rectified version. And for faces we obtain the truncations of those of the regular pre-image and, in addition, the "other" ones of the rectified form, i.e. the ones of the vertex figure of the regular pre-image.

Incidence matrix according to Dynkin symbol

x2-3-x2-4-o3

.    .    .  | 54 |  1  3 |  3 1
-------------+----+-------+-----
x2   .    .  |  2 | 27  * |  3 0
.    x2   .  |  2 |  * 81 |  1 1
-------------+----+-------+-----
x2-3-x2   .  |  6 |  3  3 | 27 *
.    x2-4-o3 ♦  6 |  0  9 |  * 9