Minimal surfaces with Platonic symmetry
WebGL
Minimal surface in the 3-sphere
Surfaces with the symmetries of Platonic solids and tesselations of the 3-sphereÂ [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
	•	
One image shows the 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.

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

Symmetric minimal surfaces
WebGL
Minimal surface in the 3-sphere
These surfaces are build by putting tubes on regular tessellations of S3Â [1]. The surfaces in the WebGL, with genus g, are
	•	5-cell g=6
	•	16-cell g=17
	•	24-cell g=73
	•	600-cell g=601

Minimal torus with Delaunay ends
WebGL
Minimal surface in the 3-sphere
Torus with eight Delaunay ends.