Folding Cubical Landscapes

A polyomino is a discrete 2D geometric object built by arranging a set of congruent squares edge to edge. Popularized by games like Tetris, polyominoes are extensively studied in recreational math, among other fields. We say a polyomino is “fenestrated” if it encloses a hole. We approach the study of fenestrated polyominoes with a background in kirigami (origami with cutting) to explore folding 3D cubical landscapes.