Acronym	...
Name	Hessian polyhedron, complex polyhedron x3-3-o3-3-o3
	©
Circumradius	sqrt(2/3) = 0.816497
Vertex figure	x3-3-o3
Dual	selfdual
Face vector	27, 72, 27
Confer	real space embedding: jak general polytopal classes: complex polytopes
External links

When considered as a regular complex polyhedron, one derives its incidence structure as follows. As the (complex) edges are x₃-3-o₃, which in turn were substructures of hex, it becomes clear that those are to be searched for there. Further the (complex) vertex figure has to be the same. Edges here clearly are complex 3-edges.

When considered instead as a snub, one derives its incidence structure as follows. Let's start with the pre-image of this operation, i.e. with x₂-4-o₃-3-o₃. Its vertex count herein will have to be halved. Edges here are obtained as subdimensionally degenerate remainders of the former faces, i.e. s₂-4-o₃. Thus there are 72, and those are 3-edges. The count of the sectioning facets underneath the removed vertices again is half of the former vertex count, in fact now the other half. These sectioning facets themselves clearly are the former vertex figures. (The remaining numbers of the incidence matrix then can easily be derived from the general incidence matrix relation.)

Incidence matrix according to Dynkin symbol

x3-3-o3-3-o3

.    .    .  | 27 ♦  8 |  8
-------------+----+----+---
x3   .    .  |  3 | 72 |  3
-------------+----+----+---
x3-3-o3   .  ♦  8 |  8 | 27

s2-4-o3-3-o3

hemi( .    .    .  ) | 27 ♦  8 |  8
---------------------+----+----+---
      s2-4-o3   .    ♦  3 | 72 |  3
---------------------+----+----+---
sefa( s2-4-o3-3-o3 ) ♦  8 |  8 | 27

starting figure: x2-4-o3-3-o3