GeometrieWerkstatt Gallery

Lawson CMC Surfaces

Lawson Surfaces

Lawson CMC

Lawson Flow 1

Lawson Flow 2

Lawson CMC Flow 0

Lawson CMC Flow 1

Lawson CMC Surface

Minimal cube

WebGL

Minimal surface in the 3-sphere

This minimal surface of genus 5, with octahedral symmetry. is built by forming tubes along a wireframe cube. The symmetry group, of order 96, is generated by the octahedral symmetry group S₄ of order 24, together with two reflections in geodesic 2-spheres. This is one of many surfaces with the symmetries of Platonic solids and tesselations of the 3-sphere [1].

Stereographic projection of the minimal cube highlighting its octahedral symmetry. The lines on the surface are curvature lines, and disks are cut out at each of the 16 umbilics, at which three curvature lines meet.

A view of the minimal cube which resembles Lawson surface ξ₂₁ of genus 2, with three handles added.

References

H. Karcher, U. Pinkall, and I. Sterling, New minimal surfaces in S³, J. Differential Geom. 28 (1988), no. 2, 169—185 [961512].