Tricorn protease is one protein with this shape, and Caspar and Klug demonstrated that the best-known proteins to take this shape are formed from 12 pentamers and a multiple of 10 hexamers.  
The innermost shell of a Bergman alloy has this shape, and alloys of gallium and alkali metals often take the shape of two of them connected together.  It is the only Frank-Kasper polyhedron containing only degree five vertices.  An orthogonal one is named after Jessen, and the cube-5 compound is formed by connecting the (*) centers of its faces.  Tricorn protease is one protein with this shape, and Caspar and Klug demonstrated that the best-known proteins to take this shape are formed from 12 pentamers and a multiple of 10 hexamers.  Fullerenes are often described as the "truncated" form of this shape. For 10 points, name this shape exhibited by many viral capsids as well as B12 and other molecules with twelve atoms, a polyhedron with twelve vertices and twenty faces.
The innermost shell of a Bergman alloy has this shape, and alloys of gallium and alkali metals often take the shape of two of them connected together.  
{icosahedron} (2) [DW]