Abstract
A wide variety of fractal gaskets have been designed from self-replicating tiles. In contrast to the most well-known
examples, the Sierpinski carpet and Sierpinski triangle, these gaskets generally have fractal outer boundaries, and the
holes in them generally have fractal boundaries. Hamiltonian cycles have been explored that trace out some of these
fractal gaskets. Novel solids have been created by spatially developing these gasket fractals over the first several
generations. Successive generations are separated in a direction orthogonal to the plane of the gasket, and simple
polygons are used to connect the external and internal edges of the gaskets. Since all of the faces in the resulting
structures are polygonal, these solids can be described as polyhedra. By varying the spacing between generations, the
form of these polyhedra can be varied, creating three-dimensional constructs evocative of architectural forms and
geological formations.
