Realizations of the abstract regular H
3 polyhedra
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Published:2022-06-10
Issue:4
Volume:78
Page:337-348
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ISSN:2053-2733
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Container-title:Acta Crystallographica Section A Foundations and Advances
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language:
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Short-container-title:Acta Cryst Sect A
Author:
Aranas Jonn Angel L.ORCID,
Loyola Mark L.
Abstract
Regular polyhedra and related structures such as complexes and nets play a prominent role in the study of materials such as crystals, nanotubes and viruses. An abstract regular polyhedron {\cal P} is the combinatorial analog of a classical regular geometric polyhedron. It is a partially ordered set of elements called faces that are completely characterized by a string C-group (G, T), which consists of a group G generated by a set T of involutions. A realization R is a mapping from {\cal P} to a Euclidean G space that is compatible with the associated real orthogonal representation of G. This work discusses an approach to the theory of realizations of abstract regular polyhedra with an emphasis on the construction of a realization and its decomposition as a blend of subrealizations. To demonstrate the approach, it is applied to the polyhedra whose automorphism groups are abstractly isomorphic to the non-crystallographic Coxeter group H
3.
Funder
Ateneo de Manila University
Science Education Institute, Department of Science and Technology, Republic of the Philippines
Publisher
International Union of Crystallography (IUCr)
Subject
Inorganic Chemistry,Physical and Theoretical Chemistry,Condensed Matter Physics,General Materials Science,Biochemistry,Structural Biology
Reference25 articles.
1. Aranas, J. A. L. (2021). Master's thesis, Ateneo de Manila University, Quezon City, Philippines.
2. Geometric realizations of abstract regular polyhedra with automorphism group H
3
3. Clancy, R. K. (2005). Master's thesis, The University of New Brunswick, New Brunswick, Canada.
4. Polyhedral model for boron nitride nanotubes
5. Geometric polyhedral models for nanotubes comprising hexagonal lattices