This is a mirror-image pair of Snub Dodecahedra (Laevo on the left, Dextro on the right). The Snub Cube also exists as a mirror-image pair. The Snub Dodecahedron is the closest to a sphere of all the Archimedean polyhedra. (Aravind, P. K.,"How Spherical Are the Archimedean Solids and Their Duals?" College Mathematics Journal, 42:2, 2011, pp. 98-107.)
The second image above is illuminated by sunlight and shows the true color and translucency.