TITLE: Looking for more "exotic" classes of polyhedra
QUESTION [5 upvotes]: I am aware of the Platonic Solids, the Archimedean Solids, the Catalan Solids, the Johnson solids, Goldberg polyhedra, deltahedra and some zonohedra.
I am interested in more names of polyhedra, specifically 3D polyhedra with iscosehedral symmetry and unit edge lengths. I do not require regular faces (as something like the rectified truncated icosahedron and the snub rhombic triacontahedron are the sort of polyhedra I am interested in). I am also interested in links to images.

REPLY [2 votes]: There are some among the symmetrohedra. In particular, I know that the one below can be realized with unique edge length, and probably others from that family can too.

The depicted one has Conway notation $\mathrm{dL_0dI}$