Lace

A lace is an informal term used to refer to any polytope formed by connecting other smaller polytopes.

Prisms are laces of two identical polytopes. Antiprisms are laces of a polytope and its dual. Pyramids are laces of a polytope and a point.

Most often, laces are used to refer to convex polytopes like segmentotopes, in which case the lace is given by a convex hull. However, the term can be applied to nonconvex polytopes as well, as long as the lace is formally specified.

Obviously the lateral facets of laces will be laces in turn. By recursion especially the sewing edges spanning between the top and bottom layer polytope are laces too. This in fact is where this term derives from: a being laced polytope.

Types of laces

 * Duopyramids lace two polytopes whose subspaces don't intersect together.
 * Wythoffian laces are laces between two Wythoffian polytopes with the same Coxeter group. It's conjectured that this construction can be done unambiguously.