Related Experiment Videos
Homogeneous cubic cylinder packings revisited
M O'Keeffe1, J Plévert, T Ogawa
1Department of Chemistry, Arizona State University, Tempe, AZ 85287, USA. mokeeffe@asu.edu
Acta Crystallographica. Section A, Foundations of Crystallography
|February 8, 2002
Summary
This study introduces a systematic method for classifying cylinder packings. It details numerous three-way and four-way arrangements, expanding knowledge of homogeneous packing configurations.
Area of Science:
- Materials Science
- Crystallography
- Geometry
Background:
- Understanding the arrangement of objects in space is crucial in various scientific fields.
- Classifying symmetrical arrangements, or homogeneous packings, of equal cylinders presents geometric challenges.
Purpose of the Study:
- To develop a systematic methodology for enumerating homogeneous packings of equal cylinders.
- To describe and categorize different types of cylinder packings based on their symmetry and axis orientation.
Main Methods:
- Development of a systematic enumeration method for homogeneous cylinder packings.
- Analysis of packings based on the orientation of cylinder axes, including <100> and <111> directions.
Main Results:
- Identification and description of 19 three-way packings with axes parallel to <100>.
- Cataloging of 40 four-way packings with axes parallel to <111>.
- Discovery of possible cubic 6-, 12-, and 24-way packings, with examples provided for <210> and <421> axes.
Conclusions:
- The developed method provides a comprehensive framework for classifying homogeneous cylinder packings.
- The findings expand the known catalogue of cylinder packing configurations, particularly for higher-order arrangements.