A concave form can be constructed with an identical net, seen as excavating trigonal trapezohedra from the top and bottom.

[1] This polyhedron could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom.

The trapezoids represent what remains of the original prism sides, and the 6 rhombi a result of the top and bottom cuts.

It is therefore related to the rhombic dodecahedron, which can be represented by turning the lower half of the picture at right over an angle of 60 degrees.

With square faces it can be seen as a cube split across the 3-fold axis, separated with the two halves rotated 180 degrees, and filling the gaps with triangles.