Plaited polyhedra: A knot theory point of view

Abstract

Plaited polyhedra, discovered by P. Gerdes in African dance rattle capsules are analyzed from the knot-theory point of view. Every plaited polyhedron can be derived from a knot or link diagram as its dual. In the attempt to classify obtained plaited polyhedra, we propose different methods based on families of knots and links in Conway notation or their corresponding braid families, both leading to the notion of families of plaited polyhedra.