Datta
, Basudeb
(2005)
*A note on the existence of {k, k}-equivelar polyhedral maps*
Contributions to Algebra and Geometry, 46
(2).
pp. 537-544.
ISSN 0138-4821

Full text not available from this repository.

Official URL: http://www.emis.de/journals/BAG/vol.46/no.2/18.htm...

## Abstract

A polyhedral map is called {p, q}-equivelar if each face has p edges and each vertex belongs to q faces. In [12], it was shown that there exist infinitely many geometrically realizable {p, q}-equivelar polyhedral maps if q > p = 4, p >q = 4 or q - 3 > p = 3. It was shown in [6] that there exist infinitely many {4, 4}- and {3, 6}-equivelar polyhedral maps. In [1], it was shown that {5, 5}- and {6, 6}-equivelar polyhedral maps exist. In this note, examples are constructed, to show that infinitely many self dual {k, k}-equivelar polyhedral maps exist for each k ≥ 5. Also vertex-minimal non-singular {p, p}-patterns are constructed for all odd primes p.

Item Type: | Article |
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Source: | Copyright of this article belongs to Heldermann Verlag. |

Keywords: | Polyhedral Maps; Equivelar Maps; Non-singular Patterns |

ID Code: | 75107 |

Deposited On: | 21 Dec 2011 14:11 |

Last Modified: | 21 Dec 2011 14:11 |

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