Geodesic Goldberg Icosahedral Polyhedron (3,3)

Icosahedral Polyhedron created using polyHédronisme v0.2.1 with the polyhedral recipes "tkt5I" or "dkdktI" to create a Geodesic Goldberg polyhedron:

Each face is either a pentagon or hexagon, exactly three faces meet at each vertex, and they have rotational icosahedral symmetry.

There are exactly 12 regular planar pentagons. This geodesic projection of a higher order Goldberg polyhedrons does not have planar hexagonal faces, though it is not noticeable at a distance.

Any pentagonal face is m + n steps away from another pentagonal face on a Goldberg polyhedron, where m and n are steps in a straight line. Since each pentagon is 3 steps in a straight line, and then another 3 steps in a different direction from another pentagon, this polyhedron is commonly identified as GP(3,3).

GP(3,3) has 540 vertices, 810 edges, and 272 faces: 12 pentagonal faces and 260 hexagonal faces.