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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...
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