Starfish Triply Periodic Minimal Surfaces

Kaleidoscopic Cells

This family of triply periodic minimal surfaces has a kaleidoscopic cell of a tetragonal disphenoid with two C2 axes. This page shows kaleidoscopic cells, which fit together by reflection to make the complete surface. This is a two-parameter family, members of which are also shown in tables of cubelets, cubic unit cells, and rhombic dodecahedra, labeled by their genus. The family may be parameterized by (p,q), where p is the number of holes along the long C2 axis, and q along the short C2 axis. 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 tetra starfish 2-2 tetra starfish 2-3 tetra starfish 2-4 tetra
Starfish 2-1 genus 31 Starfish 2-2 genus 47 Starfish 2-3 genus 63 Starfish 2-4 genus 79
starfish 3-1 tetra starfish 3-2 tetra starfish 3-3 tetra starfish 3-4 tetra
Starfish 3-1 genus 43 Starfish 3-2 genus 59 Starfish 3-3 genus 75 Starfish 3-4 genus 91
starfish 4-1 tetra starfish 4-2 tetra starfish 4-3 tetra
Starfish 4-1 genus 55 Starfish 4-2 genus 71 (fake) Starfish 4-3 genus 87 Starfish 4-4 genus 103 (?)
starfish 5-1 tetra starfish 5-2 tetra starfish 5-4 tetra
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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