Klein Quartic & the tiling atlas

Explore {P,Q}: hyperbolic polygons, Euclidean tessellations and spherical solids.

P · sidesQ · at a vertex

PaintPalette

Stretch 1.00 · manual

The construction

P sides per polygon, Q polygons at each vertex. Start with the Klein Quartic's {7,3} heptagons, then explore neighboring geometries.

About this study

An interactive geometric atlas. Paint modes, palettes and stretch change its presentation without changing the collection definitions.

Keyboard controls

Click the canvas to focus. Arrow keys change P/Q; Space starts/stops the walk; f cycles paint; r cycles palette; [ / ] change stretch; 0 resets stretch; e / s visit Euclidean / spherical cells; Esc stops; d saves WebP (the Save PNG button exports PNG).