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Elser's Surface

Elser's Surface was described by physicist Veit Elser in an article titled "A cubic Archimedean screw", in Nature. It is a triply periodic surface with cubic symmetry of group 230, which has a number of screw axes and threefold axes. ^David Hoffman recently reviewed Elser's article in Mixing Materials and Mathematics.

The figures in the left column below show surfaces for two different values of the angular parameter tau, which sweeps out a one parameter family of surfaces as illustrated by these animations of Elser's Surface.

a b
c d
Figure 1.a: A fundamental domain of Elser's surface, for tau = 0.
Figure 1.b: Line singularities: rod packing with octahedral symmetry.
Figure 1.c: A fundamental domain of Elser's surface, for tau = 30.
Figure 1.d: One of the three congruent surfaces that meet at 120 degree angles along the line singularities to form Elser's surface, for tau = 30.