If the vertices are not constrained to a sphere, the polyhedron can be constructed with planar equilateral (but not in general equiangular) faces.
Simple examples of Goldberg polyhedra include the dodecahedron and truncated icosahedron.
These variations are given Roman numeral subscripts denoting the number of sides on the non-hexagon faces: GPIII(n,m), GPIV(n,m), and GPV(n,m).
The number of vertices, edges, and faces of GP(m,n) can be computed from m and n, with T = m2 + mn + n2 = (m + n)2 − mn, depending on one of three symmetry systems:[1] The number of non-hexagonal faces can be determined using the Euler characteristic, as demonstrated here.
Most Goldberg polyhedra can be constructed using Conway polyhedron notation starting with (T)etrahedron, (C)ube, and (D)odecahedron seeds.