Geodesic Goldberg Icosahedral Polyhedron (4,0)
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Geodesic Goldberg polyhedron.
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Icosahedral Polyhedron created using polyHédronisme v0.2.1 with the polyhedral recipe "dk6k5at5daD" 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 4 steps in a single straight line from another pentagon, this polyhedron is commonly identified as GP(4,0).
GP(4,0) has 320 vertices, 480 edges, and 162 faces: 12 pentagonal faces and 150 hexagonal faces.