Glossary

area

The measure of the two‑dimensional region enclosed by a geometric figure. For polygons, area is computed from the lengths and arrangement of edges; for curved surfaces, it is determined by integration over the region.

crossing number

A measure of how many times strands of a knot or link intersect in a given projection.

crossing number: global

The total number of crossings in a polyknot or polylink. It may be computed by multiplying the local crossing number by the vertex number of the base polyhedron, or equivalently by using the quantity (V + E + F − 2) of the base polyhedron from which the structure is derived.

crossing number: local

The number of crossings contributed by a single vertex of a polyknot or polylink. This value is determined by the vertex configuration of the base polyhedron.

length

The one‑dimensional measure of a curve, edge, or path. For polyknot and polylink structures, length refers to the total extent of the entangled line segments.

perimeter

The total length around the boundary of a two‑dimensional figure. For polygons, it is the sum of all edge lengths.

polyhedron

A three‑dimensional geometric solid composed of flat polygonal faces, straight edges, and vertices. Polyhedra serve as the base forms from which many polyknot and polylink structures are derived.

polyknot

An entangled structure analogous to a classical knot but possessing polyhedral symmetry. A polyknot is constructed by routing a continuous strand along the edges or symmetry axes of a polyhedron.

polyknot Escher

A polyknot derived from a base star polyhedron, often exhibiting non‑convex geometry and complex self‑intersections.

polyknot Roelofs

A polyknot derived from a convex polyhedron, producing symmetrical entanglements based on convex polyhedra.

polylink

An entangled structure analogous to a classical link, consisting of two or more interlinked components arranged with polyhedral symmetry.

polylink Escher

A polylink derived from a star polyhedron, producing linked components with non‑convex or stellated symmetry.

polylink Roelofs

A polylink derived from a convex polyhedron, forming linked structures based on convex polyhedral geometry.

STEAM CAD

A generative and taxonomic system for producing and classifying geometric and topological structures. It emphasizes geometric composition and is used to create, analyze, and categorize polyknot and polylink forms.