TY - JOUR
T1 - Three-periodic nets and tilings
T2 - Minimal nets
AU - Bonneau, Charlotte
AU - Delgado-Friedrichs, Olaf
AU - O'Keeffe, Michael
AU - Yaghi, Omar M.
PY - 2004/11
Y1 - 2004/11
N2 - The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. (1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube into smaller tiles without introducing new vertices. Duals of such tilings with one vertex in the primitive cell have nets that are one of the minimal nets. Minimal nets without collisions are uniform.
AB - The 15 3-periodic minimal nets of Beukemann & Klee [Z. Kristallogr. (1992), 201, 37-51] have been examined. Seven have collisions in barycentric coordinates and are self-entangled. The other eight have natural tilings. Five of these tilings are self-dual and the nets are the labyrinth nets of the P, G, D, H and CLP minimal surfaces of genus 3. Twelve ways have been found for subdividing a cube into smaller tiles without introducing new vertices. Duals of such tilings with one vertex in the primitive cell have nets that are one of the minimal nets. Minimal nets without collisions are uniform.
UR - http://www.scopus.com/inward/record.url?scp=19744374069&partnerID=8YFLogxK
U2 - 10.1107/S0108767304015442
DO - 10.1107/S0108767304015442
M3 - Article
SN - 0108-7673
VL - 60
SP - 517
EP - 520
JO - Acta Crystallographica Section A: Foundations of Crystallography
JF - Acta Crystallographica Section A: Foundations of Crystallography
IS - 6
ER -