Rhombic Triacontahedron Built on a Cube
A solid rhombic triacontahedron (RT) can be built from a cube and six rhombic dodecahedron (RD) halves. You can move half RDs away from the surface of the cube. Cylinders are included to indicate a possible arrangement of an openable structure. Note the interesting relationship of the volumes: if the edge of the cube is 2, then the volume of a half RD is 2, and so the volume of the triacontahedron is (2x2x2) + (6x2) = 20.