Retoponogo

Published May07 2024.

Update (May08 2024): added puzzle Triangulated Satellite.

Update (Jun29 2024): added puzzles Farfalline and Joinery.

Update (Jun29 2024): check out the Kudamono implementation!

Update (Jun29 2024): check out PuzzleSquareJP's genre listing!

Update (Jan26 2025): added puzzle Fountains.

Update (Feb04 2025): added puzzle Midiponogo, inspired by a puzzle by ハイシェシニシィ.

Update (Feb19 2025): fixed non-uniqueness in Farfalline spotted by てけてけ.

Summary

Construct a mesh without splitting apart edges.

Background information and credits

Inspired by the dazzling quirks of retopology.

Thanks to Eric Fox for the useful phrase "divide the grid into regions".

Playtesters:

Divide the grid into regions using cardinal and ordinal edges.

Each region contains exactly one numbered cell, which indicates the region's side count.
Regions must be simple polygons (no holes, no self-intersection).
Edges must not intersect numbered cells.
Edge paths must not travel straight through junctions.

Example

A demonstration of the fourth rule: an intersection cannot contain two edges facing the same direction.

Incorrect:

Correct:

Given borders count as region sides, but may travel straight through a junction.