GeometrieWerkstatt Gallery

Lawson CMC Surfaces

Lawson Surfaces

Lawson Surfaces

Lawson Surfaces

Lawson Surfaces

Lawson CMC

Lawson CMC

Lawson Flow 1

Lawson Flow 2

Lawson CMC Flow 0

Lawson CMC Flow 1

Lawson CMC Surface

Platonic

Symmetric

Ends

Minimal surfaces with Platonic symmetry

Minimal surface in the 3-sphere

Surfaces with the symmetries of Platonic solids and tesselations of the 3-sphere [1]. The surfaces in the WebGL, with genus g, are

tetrahedron g=3
octahedron g=7
cube g=5
octahedral join g=11
icosahedron g=19
dodecahedron g=11
icosahedron join g=29

Stereographic projection of the minimal cube highlighting its octahedral symmetry. 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. 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.

References

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