"Pentagonal Dyck Cycle"  by  Carlo H. Séquin  (2017)

23cm x 25cm x 17cm; ABS plastic, shaped by Fused Deposition Modeling

For several years I have been an admirer of the Swedish sculptress Eva Hild.
The above sculptures is part of my "Homage to Eva Hild" -- a presentation that I will give at the Annual Bridges Math-Art conference.  This sculpture model has also been accepted into the Nominees' Gallery of the accompanying Exhibition of Mathematical Art.

A majority of  Eva Hild's sculptures are two-sided, orientable 2-manifolds. My goal was to design a non-orientable 2-manifold sculpture, like a Möbius band, that, by its style, would fit into Hild's family. A good starting point was Dyck's surface (an elliptical disk from which two two tubular stubs protrude on opposite sides).   A cycle with an odd number of such elements will produce a single-sided surface.  In this sculpture, five such elements of varying sizes have been connected into a cycle to yield a single-sided surface matching in style some of Eva Hild's sculptures. To ease the transition from the smallest to the largest Dyck ellipse, a spherical nodule has been introduced, as can be found in Hild's "Hålrum" sculpture in Vaarberg, Sweden.

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