Isogonal polyhedron is a polyhedron whose vertices are transitive under transformation of polyhedron's symmetry group. The well-known 76 uniform polyhedra are isogonal polyhedra with additional restriction - polyhedral faces may be only regular polygons. Isogonal polyhedra are much more numerous and in fact usually they form a continuous families of topologically equivalent shapes. To date there were few systematic attempts to classify or enumerate all such families.