Triaugmented truncated dodecahedron

In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids (J₇₁); of them, it has the greatest volume in proportion to the cube of the side length. As its name suggests, it is created by attaching three pentagonal cupolas (J₅) onto three nonadjacent decagonal faces of a truncated dodecahedron.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.