# 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 Copyright of this article belongs to Heldermann Verlag. Polyhedral maps;polyhedral 2-manifold. Division of Physical & Mathematical Sciences > Mathematics 21 Jul 2008 19 Sep 2010 04:47 http://eprints.iisc.ernet.in/id/eprint/15135