The City College of New YorkCCNY
Department of Mathematics
Division of Science

New results on the dodecahedron

Picture of a dodecahedron with a closed straight-line path

Unlike the other platonic solids, the dodecahedron has a straight-line path (geodesic) from a vertex to itself. Actually, there are infinitely many, but in joint work of Prof. Hooper with Prof. Athreya (Univ. of Washington) and Prof. Aulicino (Brooklyn College), it was shown there are exactly 31 such paths up to certain “hidden symmetries.” The picture above shows one which can also be animated. This work was described recently in Quanta Magazine.

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