[1] There are five uniform ditrigonal polyhedra, all with icosahedral symmetry.
[1] The three uniform star polyhedron with Wythoff symbol of the form 3 | p q or 3/2 | p q are ditrigonal, at least if p and q are not 2.
Each polyhedron includes two types of faces, being of triangles, pentagons, or pentagrams.
Their vertex configurations are of the form p.q.p.q.p.q or (p.q)3 with a symmetry of order 3.
Here, term ditrigonal refers to a hexagon having a symmetry of order 3 (triangular symmetry) acting with 2 rotational orbits on the 6 angles of the vertex figure (the word ditrigonal means "having two sets of 3 angles").