Triaugmented truncated dodecahedron
In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids. Of them, it has the greatest surface area and volume for a given side length, as well as the greatest numbers of edges and vertices; it is tied for the greatest number of faces with [gyrate rhombicosidodecahedron|], [parabigyrate rhombicosidodecahedron|], [metabigyrate rhombicosidodecahedron|], and [trigyrate rhombicosidodecahedron|]. As its name suggests, it is created by attaching three pentagonal cupolas onto three nonadjacent decagonal faces of a truncated dodecahedron.