Realizations of the abstract regular H3 polyhedra
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 is the combinatorial analog of a classical regular geometric polyhedron. It is a partially ordered set of eleme...
محفوظ في:
| المؤلفون الرئيسيون: | , |
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| التنسيق: | text |
| منشور في: |
Archīum Ateneo
2022
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://archium.ateneo.edu/mathematics-faculty-pubs/222 https://doi.org/10.1107/S2053273322003874 |
| الوسوم: |
إضافة وسم
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| المؤسسة: | Ateneo De Manila University |
| الملخص: | 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 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 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 H3. |
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