The Edge-minimal Polyhedral Maps of Euler Characteristic –8

Brehm, Ulrich and Datta, Basudeb and Nilakantan, Nandini (2002) The Edge-minimal Polyhedral Maps of Euler Characteristic –8. In: Contributions to Algebra and Geometry, 43 (3). pp. 583-596.

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Abstract

In [2], a \{5, 5\}-equivelar polyhedral map of Euler characteristic −8 was constructed. In this article we prove that \{5, 5\}-equivelar polyhedral map of Euler characteristic −8 is unique. As a consequence, we get that the minimum number of edges in a non-orientable polyhedral map of Euler characteristic −8 is > 40. We have also constructed \{5, 5\}-equivelar polyhedral map of Euler characteristic −2m for each m \geq 4.

Item Type:	Journal Article
Publication:	Contributions to Algebra and Geometry
Publisher:	Heldermann Verlag
Additional Information:	Copyright of this article belongs to Heldermann Verlag.
Keywords:	Polyhedral maps;polyhedral 2-manifold.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	21 Jul 2008
Last Modified:	19 Sep 2010 04:47
URI:	http://eprints.iisc.ac.in/id/eprint/15135

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