TY - JOUR
T1 - Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings
AU - Hyde, S. T.
AU - Ramsden, S.
PY - 2003
Y1 - 2003
N2 - We demonstrate the usefulness of two-dimensional hyperbolic geometry as a tool to generate three-dimensional Euclidean (E3) networks. The technique involves projection of edges of tilings of the hyperbolic plane (H2) onto three-periodic, minimal surfaces, embedded in E 3. Given the extraordinary wealth of symmetries commensurate with H2, we can generate networks in E3 that are difficult to construct otherwise. In particular, we form four-, five- and seven-connected (E3) nets containing three- and five-rings, viz. (3, 7), (5, 4) and (5, 5) tilings in H2.
AB - We demonstrate the usefulness of two-dimensional hyperbolic geometry as a tool to generate three-dimensional Euclidean (E3) networks. The technique involves projection of edges of tilings of the hyperbolic plane (H2) onto three-periodic, minimal surfaces, embedded in E 3. Given the extraordinary wealth of symmetries commensurate with H2, we can generate networks in E3 that are difficult to construct otherwise. In particular, we form four-, five- and seven-connected (E3) nets containing three- and five-rings, viz. (3, 7), (5, 4) and (5, 5) tilings in H2.
UR - http://www.scopus.com/inward/record.url?scp=2942550830&partnerID=8YFLogxK
U2 - 10.1140/epjb/e2003-00032-8
DO - 10.1140/epjb/e2003-00032-8
M3 - Article
SN - 1434-6028
VL - 31
SP - 273
EP - 284
JO - European Physical Journal B
JF - European Physical Journal B
IS - 2
ER -