This is somehow derived from a triangulation of a cube, and turns out to be as well the glue between a 5-bipyramid and a tetrahedron.
vertices: 8
faces: 12
edges: 18
genus: 0
characteristic polynomial:
(-1 + x + x2) (-5 + 23x + 30x2 - 11x3 - 16x4 - x5 + x6)
dual's characteristic polynomial:
(-3 + x) x2 (-4 - 9x - 2x2 + 3x3 + x4) (-4 + 11x + x2 - 7x3 + x5)
chromatic number: 3
lattice group :
A(36)