20 faceted (regular) polyhedron is a icosahedron - all facets have equal size. There are variations which have more specific names (where certain facets have irregular shapes) An interesting site to look at is polyhedra.org which shows 6 other variations of 20 faceted polyhedrons: 1. gyroelongated triangular cupola
2. parabiaugmented dodecahedron 3. metabiaugmented dodecahedron
4.triangular hebesphenorotunda
5.gyroelongated triangular cupola
6. elongated triangular orthobicupola
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