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.
I can recommend these: