Simpler Tests for Semisparse Subgroups |
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Authors: | Michael I Hartley |
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Institution: | (1) Faculty of Engineering and Computer Science, University of Nottingham Malaysia Campus, Jalan Broga, Semenyih, 43500 Selangor, Malaysia |
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Abstract: | The main results of this article facilitate the search for quotients of regular abstract polytopes. A common approach in the
study of abstract polytopes is to construct polytopes with specified facets and vertex figures. Any nonregular polytope
may be constructed as a quotient of a regular polytope
by a (so-called) semisparse subgroup of its automorphism group W (which will be a string C-group). It becomes important, therefore, to be able to identify whether or not a given subgroup N of a string C-group W is semisparse. This article proves a number of properties of semisparse subgroups. These properties may be used to test for
semisparseness in a way which is computationally more efficient than previous methods. The methods are used to find an example
of a section regular polytope of type {6, 3, 3} whose facets are Klein bottles.
Received February 15, 2005 |
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Keywords: | 51M20 52B15 05E25 |
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