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I'm not looking for pieces in which math related object appears with allegoric meanings, but works which aim to to have mathematical objects as principal subjects.

Specifically, I was wondering if anyone knows nice rapresentations (in the non-mathematics sense) of finite small group, with an aesthetic intent beside a faithfulness one.

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  • $\begingroup$ Fractals are usually the first example people mention, although that's not about small finite groups. Cayley graphs are somewhat aesthetic, if you're into that sort of things. $\endgroup$ Commented Oct 25, 2017 at 12:41
  • $\begingroup$ See Durer's Melencolia I. $\endgroup$ Commented Oct 25, 2017 at 13:28
  • $\begingroup$ I was wondering if anyone has gone any further in Cayley graphs' direction, beyond an useful sketch to visualize the group's structure, toward an actual artistic purpose. $\endgroup$ Commented Oct 25, 2017 at 15:03

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The drawings of M.C.Escher immediately come to mind.

See this nice paper on the subject.

EDIT

Also check these very interesting and illuminating articles posted below (comment section) by user Quasicoherent-

"Artful Mathematics: The Heritage of M. C. Escher Celebrating Mathematics Awareness Month"

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    $\begingroup$ Here's another paper and accompanying website on one of Escher's works. $\endgroup$ Commented Oct 25, 2017 at 13:05
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    $\begingroup$ @Quasicoherent Very nice and more rigorous than the one I posted. I will edit the answer to refer to your comment. Thank you for this. $\endgroup$ Commented Oct 25, 2017 at 13:08
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If you're interested in higher group theory, check out Anatoly Fomenko:

Simplicial spaces, cellular spaces, crystal and liquid

Homotopy groups of spheres; Discrete groups generated by reflections

Spectral sequences and orbits of the action of groups; A 2-adic solenoid

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