# Groups in an abstract algebra

I have been thinking my brain to find three different examples for a shape S in the plain, such that its group of symmetries is infinite.Also I was asked to draw each shape clearly why its group of symmetries is infinite.

my answer: I think circle is one shape that has its symmetries is infinite.

Can anyone help me to with hints to discover some more shapes such that its group of symmeties is infinite

Thank you in advance for help

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What is the group of symmetries of an infinitely long string. (ie. $\mathbb{R} \subset \mathbb{R}^2$)? Or a single hexagon repeating itself indefinitely on all sides. – Prahlad Vaidyanathan Aug 28 '13 at 9:00

You can have fun with other infinite groups. Think of the group generated by a single rotation by an angle that is irrational to the full rotation by $2\pi$.