A subdivision of this sort if called reticulation.
vertices: 10
faces: 16
edges: 24
genus: 0
characteristic polynomial:
(2 + x)2 (-6 - 4x + x2)3 (-2 + x2)3
dual's characteristic polynomial:
(-3 + x) (-1 + x)3 (1 + x)6 (-5 + x2)3
chromatic number: 3
lattice group:
((C4 × C4) : C3) : C2