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July 5

How to categorize these images?

I recently uploaded these two images to supplement the four referenced in the Fundamental polygon article. What categories should I put them in? In particular, I don't know if they're actually fundamental polygons or not: it's been a while since I've proven that something is a closed surface. Jbeyerl (talk) 17:37, 5 July 2014 (UTC)[reply]

It's not definite, but I lean against those ending up being manifolds. The group representation for the first would be A² = 1, and the second would be A²B⁻² = 1. — Arthur Rubin (talk) 01:17, 8 July 2014 (UTC)[reply]

A² = 1 is the projective plane. For the second, by cutting diagonally from the top left to the bottom right, then gluing along A, you get the standard presentation of the Klein bottle.--Antendren (talk) 04:42, 8 July 2014 (UTC)[reply]