Acronym	...
Name	Shephard's 4-generalised hexadecachoron, complex polychoron x2-3-o2-3-o2-4-o4, β44
	©
Vertex figure	x2-3-o2-4-o4
Coordinates	(in, 0, 0, 0)   & all permutations, each for any 1≤n≤4
Dual	x4-4-o2-3-o2-3-o2
Face vector	16, 96, 256, 256
Confer	more general: x2-3-o2-3-o2-4-op   general polytopal classes: complex polytopes
External links

This complex polychoron is somewhat special in so far as its edges, faces, and calls all are degenerate, i.e. remain real space polytopes only. However, its vertex figure is the truely complex polyhedron x₂-3-o₂-4-o₄. Thence it still remains embeddable into a real space polyzetton, in fact into the tegum product of 4 (fully orthogonal) squares. In fact the to be chosen cells are just the lacing tets, which have one vertex on each of those squares.

Incidence matrix according to Dynkin symbol

x2-3-o2-3-o2-4-o4

.    .    .    .  | 16 ♦ 12 |  48 |  64
-----------------+----+----+-----+----
x2   .    .    .  |  2 | 96 ♦   8 |  16
-----------------+----+----+-----+----
x2-3-o2   .    .  |  3 |  3 | 256 |   4
-----------------+----+----+-----+----
x2-3-o2-3-o2   .  ♦  4 |  6 |   4 | 256