Fully transitive polyhedra with crystallographic symmetry groups
| dc.contributor.advisor | Hempel, John | en_US |
| dc.creator | Eisenlohr, John Merrick | en_US |
| dc.date.accessioned | 2009-06-04T00:38:22Z | en_US |
| dc.date.available | 2009-06-04T00:38:22Z | en_US |
| dc.date.issued | 1990 | en_US |
| dc.description.abstract | This dissertation sets forth a method for classifying, up to euclidean similarity, fully-transitive polyhedra which have crystallographic symmetry groups. Branko Grunbaum's definition of polyhedron is used, in which the faces are "hollow" - i.e., a face is a collection of edges. The approach is algorithmic: in a euclidean space $R\sp{n}$, assume we have classified the crystallographic groups up to conjugation by similarity transformations. For each similarity class of groups G, we follow a procedure which will generate all polyhedra in $R\sp{n}$ on which G acts fully-transitively. The method also assures that there is no duplication of examples. Following the presentation of this method, there is a discussion of the topology of these polyhedra. It is shown how to associate a non-compact surface with each polyhedron, and how to determine where this surface fits in the classification of non-compact 2-manifolds. Following this discussion, the method described is applied to the case of 2-dimensional crystallographic groups, and a complete classification of fully-transitive tilings is obtained. | en_US |
| dc.format.extent | 142 p. | en_US |
| dc.format.mimetype | application/pdf | en_US |
| dc.identifier.callno | Thesis Math. 1990 Eisenlohr | en_US |
| dc.identifier.citation | Eisenlohr, John Merrick. "Fully transitive polyhedra with crystallographic symmetry groups." (1990) Diss., Rice University. <a href="https://hdl.handle.net/1911/16340">https://hdl.handle.net/1911/16340</a>. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1911/16340 | en_US |
| dc.language.iso | eng | en_US |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Fully transitive polyhedra with crystallographic symmetry groups | en_US |
| dc.type | Thesis | en_US |
| dc.type.material | Text | en_US |
| thesis.degree.department | Mathematics | en_US |
| thesis.degree.discipline | Natural Sciences | en_US |
| thesis.degree.grantor | Rice University | en_US |
| thesis.degree.level | Doctoral | en_US |
| thesis.degree.name | Doctor of Philosophy | en_US |
Files
Original bundle
1 - 1 of 1