Acronym ...
Name Shephard's 5-generalised cuboctahedron,
complex polyhedron o5-4-x2-3-o2
 
 ©
Vertex figure x5   x2
Coordinates 5n, ε5m, 0)   & all permutations, each for any 1≤n,m≤5, where ε5=exp(2πi/5)
Face vector 75, 375, 140
Confer
more general:
op-4-x2-3-o2  
general polytopal classes:
complex polytopes  
External
links
wikipedia  

Applying rectification onto either of x5-4-o2-3-o2 or x2-3-o2-4-o5 in the respectively other direction each, re-uses the former edge counts for new vertex count, and uses the duals of the faces each (somewhere further out) as the two face types in here. Alternatively those additional face types could be obtained as the respective vertex figures of the pre-images each. Edges themselves in here are 2-fold, as can be read from the symbol directly, i.e. are down to real ones again.


Incidence matrix according to Dynkin symbol

o5-4-x2-3-o2

.    .    .  | 75   10 |  2   5
-------------+----+-----+-------
.    x2   .  |  2 | 375 |  1   1
-------------+----+-----+-------
o5-4-x2   .   10 |  25 | 15  *
.    x2-3-o2 |  3 |   3 |  * 125

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