Starfish Triply Periodic Minimal Surfaces

Cubic Unit Cells

This family of triply periodic minimal surfaces has a kaleidoscopic cell of a tetragonal disphenoid with two C2 axes. This page shows cubic unit cells made of four cubelets; cubelets fit together in a face-centered-cubic lattice to make the complete surface. The cube is actually a unit cell for the unoriented surface; for the oriented surface, the unit cell is twice as big. This is a two-parameter family, members of which are also shown in tables of kaleidoscopic cells, cubelets, and rhombic dodecahedra, labeled by their genus. The family may be parameterized by (p,q), where p is the number of holes along the cubelet edge, and q along the cubelet diagonal. Putative members of the family may not actually exist; attempts to get all the edges of the fundamental region to match up properly (called "period killing" by the cognoscenti) may leave a gap. Starfish 4-2 fails to period kill by only 0.005 (so far).

For Surface Evolver datafiles, get starfish.tar and see Readme.txt therein.


Starfish 2-1 genus 31	Starfish 2-2 genus 47	Starfish 2-3 genus 63	Starfish 2-4 genus 79

Starfish 3-1 genus 43	Starfish 3-2 genus 59	Starfish 3-3 genus 75	Starfish 3-4 genus 91

Starfish 4-1 genus 55	Starfish 4-2 genus 71 (fake)	Starfish 4-3 genus 87	Starfish 4-4 genus 103 (?)

Starfish 5-1 genus 67	Starfish 5-2 genus 83 (not quite)	Starfish 5-3 genus 99 (?)	Starfish 5-4 genus 115

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