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Updated: May 11, 2026
06:35
Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
Published on: February 15, 2016
On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry
1Laboratory for Inorganic Chemistry, ETH Zürich, Universitätstrasse 6, 8092 Zürich, Switzerland. nesper@inorg.chem.ethz.ch
Summary
Researchers explored hyperbolic periodic nodal surfaces (PNSs) for pattern generation. This method offers simple symmetry control for creating complex hyperbolic textures and frameworks.
Area of Science:
- Mathematics
- Crystallography
- Materials Science
Background:
- Hyperbolic objects and their textures are complex to model.
- Periodic Nodal Surfaces (PNSs) offer a structured approach to understanding hyperbolic geometry.
- Previous methods for generating hyperbolic frameworks can be overly complex.
Purpose of the Study:
- To investigate surface modulations on Hyperbolic Periodic Nodal Surfaces (PNSs).
- To demonstrate a method for controlling symmetry and complexity in hyperbolic patterns.
- To establish a simpler approach for generating three-dimensional hyperbolic frameworks.
Main Methods:
- Utilizing short Fourier series for pattern construction on PNSs.
- Selecting specific sets of structure factors for symmetry control.
- Adjusting structure factor moduli to tailor pattern complexity.
Main Results:
- Generated beautiful examples of texture information on hyperbolic objects.
- Achieved strict symmetry control through chosen structure factors.
- Demonstrated tailor-made complexity design via structure factor moduli selection.
- Showcased the transfer of patterns into hyperbolic framework information, aided by crystallographic and chemical expertise.
Conclusions:
- The Fourier series-based approach simplifies the generation of hyperbolic patterns and frameworks.
- The method allows for precise control over symmetry and complexity.
- This approach is more accessible than many existing methods for creating 3D hyperbolic structures.
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