Starfish Triply Periodic Minimal Surfaces

Rhombic Dodecahedra

This family of triply periodic minimal surfaces has a kaleidoscopic cell of a tetragonal disphenoid with two C2 axes. This page shows rhombic dodecahedron unit cells (for the oriented surface) made out of 24 kaleidoscopic cells. The dodecahedron faces are mirror symmetry planes, and the dodecahedra fit together in a face-centered cubic lattice to make the complete surface. This is a two-parameter family, members of which are also shown in tables of kaleidoscopic cells, cubelets, cubic unit cells. 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 rhomb starfish 2-2 rhomb starfish 2-3 rhomb starfish 2-4 rhomb
Starfish 2-1 genus 31 Starfish 2-2 genus 47 Starfish 2-3 genus 63 Starfish 2-4 genus 79
starfish 3-1 rhomb starfish 3-2 rhomb starfish 3-3 rhomb starfish 3-4 rhomb
Starfish 3-1 genus 43 Starfish 3-2 genus 59 Starfish 3-3 genus 75 Starfish 3-4 genus 91
starfish 4-1 rhomb starfish 4-2 rhomb starfish 4-3 rhomb
Starfish 4-1 genus 55 Starfish 4-2 genus 71 (fake) Starfish 4-3 genus 87 Starfish 4-4 genus 103 (?)
starfish 5-1 rhomb starfish 5-2 rhomb starfish 5-3 rhomb
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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