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I would like to see a quadrilateral in the hyperbolic plane which has $4$ equal angles but is not regular. Can someone tell me an example?

I know that this is impossible for triangles, but I think that this should be different for quadrilaterals. Unfortunately I could not find any book where this is explained.

Best wishes

  • 1
    What about a rectangle. – 2017-01-08

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Take a line segment $PQ$. Draw segments perpendicular to the endpoints, with equal distances $\delta$ above $PQ$ and below $PQ$, making a letter $H.$ Join the pairs of $H$ endpoints, resulting in a sort of number $8$ or capital $\theta$. This quadrilateral has four equal angles. Unless $\delta $ is a very special value, this is not regular.