From an article* in Proceedings of Bridges 2014 —
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As artists, we are particularly interested in the symmetries of real world physical objects. Three natural questions arise: 1. Which groups can be represented as the group of symmetries of some real-world physical object? 2. Which groups have actually been represented as the group of symmetries of some real-world physical object? 3. Are there any glaring gaps – small, beautiful groups that should have a physical representation in a symmetric object but up until now have not? |
The article was cited by Evelyn Lamb in her Scientific American
weblog on May 19, 2014.
The above three questions from the article are relevant to a more
recent (Oct. 24, 2015) remark by Lamb:
"… finite projective planes [in particular, the 7-point Fano plane,
about which Lamb is writing] seem like a triumph of purely
axiomatic thinking over any hint of reality…."
For related hints of reality, see Eightfold Cube in this journal.
* "The Quaternion Group as a Symmetry Group," by Vi Hart and Henry Segerman