Flatbunnete

Flatbunnete is a fictional term used in a hypothetical treatment of planar tilings and origami-inspired nets. It refers to a class of planar tiling patterns arranged so that the tiles collectively form a single connected net that can be laid flat without gaps or overlaps. The concept is used primarily in thought experiments, education, and design exercises rather than as an established mathematical theory.

Construction: Each flatbunnete pattern is built from modular units, interiorly matched to allow interlocking edges or compatible crease lines. When multiple units are combined in a repeating lattice, the resulting arrangement preserves planarity and yields a net-like boundary that can be traced without crossings.

Variations: Descriptions of flatbunnete patterns vary; common variants include grid-based tilings with rectangular or rhomboidal modules, as well as more complex polygonal units that maintain a flat net. Some versions emphasize symmetry, while others explore asymmetrical interlocks.

Applications: Since it is fictional, flatbunnete serves as a didactic device in teaching tiling theory, algorithmic folding, and puzzle design. It can be used to illustrate constraints on edge compatibility, net flattening, and the relationship between tiling and folding in computational graphics and architectural prototyping.

See also: tiling, nets (origami), origami mathematics, computational geometry, puzzle design.