Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples

被引：120

作者：

Ramsden, S. J. ^{[1
]}

Robins, V. ^{[1
]}

Hyde, S. T. ^{[1
]}

机构：

[1] Australian Natl Univ, Dept Appl Math, Res Sch Phys & Engn, Canberra, ACT 0200, Australia

来源：

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES | 2009年 / 65卷

关键词：

RETICULAR CHEMISTRY; ENUMERATION; FRAMEWORKS; SPHERE;

D O I：

10.1107/S0108767308040592

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

We present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct vertices), mapped to three related TPMSs, namely Schwarz's primitive (P) and diamond (D) surfaces, and Schoen's gyroid (G).

引用

页码：81 / 108

页数：28