Rhombic hexecontahedron

[1] It is topologically identical to the convex deltoidal hexecontahedron which has kite faces.

The rhombic hexecontahedron can be dissected into 20 acute golden rhombohedra meeting at a central point.

Thus, if the 20 vertices of a dodecahedron are pulled out to increase the circumradius by a factor of ⁠φ + 1/2⁠ ≈ 1.309, the 12 face centers are pushed in to decrease the inradius to ⁠3 − φ/2⁠ ≈ 0.691 of its original value, and the 30 edge centers are left unchanged, then a rhombic hexecontahedron is formed.

Scaling the points by different amounts results in hexecontahedra with kite-shaped faces or other polyhedra.

Its stellation diagram looks like this, with the original rhombic triacontahedron faces as the central rhombus.

The custom got lost with the urbanization of Brazil, though the technique for producing the handicrafts was still taught in Brazilian rural schools up until the first half of the twentieth century.

3D model of a rhombic hexecontahedron
A rhombic hexecontahedron can be constructed from a rhombic triacontahedron.