5 papers
Escher's Cubes: Tiling the Faces of Polyhedra
Peter Kagey, William Keehn
Isohedral or face-transitive polyhedra are polyhedra with identical faces, such that any face can be mapped onto any other via a symmetry of the polyhedron. Examples include the Pl…
Building with Blocks: Enumerating Polyforms on Tilings
Bert Dobbelaere, Peter Kagey, Drake Thomas +1
In areas as diverse as contemporary art, play structures, climbing equipment, and modular construction toys, we see the presence of building block-like polyhedral complexes, which…
Counting tilings of the grid, cylinder, and torus
Peter Kagey, William Keehn
We count tilings of the rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifti…
A Proof Without Words: Triangles in the Triangular Grid
Peter Kagey
This proof without words demonstrates that there are equilateral triangles in the regular -vertices-per-side triangular grid by describing a map from four-eleme…
Spinning switches on a wreath product
Peter Kagey
We classify an algebraic phenomenon on certain families of wreath products that can be seen as coming from a family of puzzles about switches on the corners of a spinning table. Su…