Acronym	...
Name	complex polyhedron x2-4-o3-3-o3
Circumradius	1
Vertex figure	x3-4-o2
Coordinates	(ε3n, ε3m, ε3k)/sqrt(3)        & for any 1≤n,m,k≤3 (-ε3n, -ε3m, -ε3k)/sqrt(3)    & for any 1≤n,m,k≤3 where: ε3=exp(2πi/3)=(-1+i sqrt(3))/2
Dual	x3-3-o3-4-o2
Face vector	54, 216, 72
Confer	real space embedding: o3o3o3o3o *c3m general polytopal classes: complex polytopes
External links

This complex polyhedron not only is the formal dual of the complex polytope x₃-3-o₃-4-o₂, but also its real space embedding is the dual of that there given one, i.e. it is o3o3o3o3o *c3m. As the edges in this complex polyhedron are 2-fold and thence just real ones, these edges are to be searched as a subset of the real polypeton's edges. The complex faces however are full dimensional and already are described to be embedded in triddits, which in turn are the polychoral elements of that real polypeton, a subset of which here then is to be chosen.

By application of duality, the incidence matrix thence is simply the same as of its dual x₃-3-o₃-4-o₂, just rotated 180° around.

Since s₂-4-o₃-3-o₃ comes out to be nothing but x₃-3-o₃-3-o₃, it furthermore becomes evident that the vertex set of the complex polyhedron in here is nothing but two mutually inverted copies of the vertices of that one (within conformance that its real space embedding likewise is known to be the tegum sum of 2 inverted jaks). In fact, the 2-edges in here simply connect any vertex of the one to one out of the 8 nearest vertices of the other. Within the above provided metrics accordingly these in here re-used lacing edges are assumed to have unit lengths.

Incidence matrix according to Dynkin symbol

x2-4-o3-3-o3

.    .    .  | 54 ♦   8 |  8
-------------+----+-----+---
x2   .    .  |  2 | 216 |  3
-------------+----+-----+---
x2-4-o3   .  ♦  6 |   9 | 72

snubbed forms: s2-4-o3-3-o3