an:06779346
Zbl 1370.52061
O'Keeffe, Michael
Three-periodic nets and tilings: regular and related infinite polyhedra
EN
Acta Crystallogr., Sect. A 64, No. 3, 425-429 (2008).
00370061
2008
j
52C22 51M20 82D25
infinite polyhedra; nets; tilings
Summary: The six infinite regular (flag-transitive) polyhedra with finite faces of Gr??nbaum and Dress are described as tilings of the \(P\) and \(D\) periodic minimal surfaces. The three polyhedra formed by analogous tiling of the \(G\) surface are also described. The nets of these polyhedra are identified. It is shown how these polyhedra, and the nets they carry, could be found by mining the EPINET database of structures. The nets of regular three-periodic polyhedra with infinite helical or zigzag faces are also identified.