The degrees of freedom I use in the datafiles are the lengths of the boundary edges of the fundamental region; starfish p-q has p+q-1 independent degrees of freedom, and there are p+q-1 gaps to eliminate. Unfortunately, the mapping from parameter space to gap space is sometimes highly nonlinear in the neighborhood of a solution, making finding the solution (if it even exists) difficult. And it means that there may be multiple solutions, although I have not found any yet.

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

Starfish 2-1 genus 31 Buy | 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 (not quite) |
Starfish 5-4 genus 115 |

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