Simple tilings by polyhedra with five- and six-sided faces

Thirteen tilings of space by simple polyhedra with five- and six-sided faces (`fullerenes') are reported in which there are up to 11 kinds of vertex (vertex 11-transitive). All tilings contain dodecahedra and one or more of nine other kinds of tile. The duals are tilings by tetrahedra and include the four simplest of the known Frank-Kasper intermetallic structure phases. A fifth structure involving just the Frank-Kasper coordination polyhedra has a higher average coordination number than any known or postulated Frank-Kasper phase.