I was watching this video on Abstract Algebra and the professor was discussing how at one point a few mathematicians conjectured the special orthogonal group in ##\mathbb{R}^3## mod the symmetries of an icosahedron described the shape of the universe (near the end of the video).(adsbygoogle = window.adsbygoogle || []).push({});

My question is, what shape does ##SO(3)/A_5## describe? Also, I just started a course in algebraic topology so forgive my ignorance; but, is it correct to say that a good way to try and picture this shape would be to imagine shrinking all the points in ##SO(3)## corresponding to a rotational symmetry of an icosahedron to a point? If I understand correctly this would produce something in ##\mathbb{R^4}##.

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# Algebraic Topology: SO(3)/A5

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