Complimentary: two objects that are heteromorphs yet share a common structural component

example: the two Heteromorphic Monocycles below are complimentary

Composition: the objects used to construct a structure

example: the Heteromorphic Monocycle below is composed of polygons (squares and regular pentagons)

Chromoticity number: number of colors necessary to reveal the structural elements of a given topological structure

example: the Heteromorphic Monocycle below has a chromoticity number of five

Cycle: a ring topological structure that is either a knot, link, torus or Mobius strip

Discrete Annulus: a closed cyclic topological structure with a positive annulus number

example:

example: the torus below is a Heterogenous Monocycle

Heteromorph: two or more objects that have a different shape or morphology

example: the first structure (a) is a heteromorph to the second (b)

(a)

(b)

Homomorph: two or more objects that have the same shape or morphology

example: the sieve below is homomorphic to the Knotted Mobius strip next to it

Knot: an open or closed interwoven topological structure with a positive knot number

example:

Knot number: the number of crossing in a knot

example:

Link: two or more interwoven (i.e. with a positive link number) though unattached tori

example: the link below

Link number: the number of crossings in a link

example: the link below has a link number of 6

Mathematical property: a quantitative or qualitative feature of a topological structure that contributes to its identity

example:

Mobius strip: a closed topological structure with a positive Mobius number

example: the Mobius strip below is single sided i.e. odd numbered with a twist number or Mobius number of 5

Mobius number: the number of twists a topological structure has such as in a Mobius strip

example: In the example below the Mobius strip has five twists that corresponds to its chromoticity number

Nomenclature: In Geometric Topology a binary system based on composition and structure

example: Heteromorphic Monocycle

Ontology: a catalog of objects

example: this web page

Physical analog: the physical object that corresponds to the mathematical object

example:

or the Homohexagonal Monocycle:

Diagram of Coronene and physical analog of 6^6 above

Polycycle: a multiringed topological structure

example: a sieve with a sieve number of 4

Polygonal Knot: an open or closed topological structure with a positive knot number (greater than 0) and whose composition is that of polygons

example:

Polygonal Link: an open or closed topological structure with positive link number (greater than 0) and whose composition is that of polygons.

example:

Polygonal Mobius Strip: an open or closed topological structure with a positive Mobius number (greater than 0) and whose composition is that of polygons.

example:

Polygonal Annulus: a closed topological structure with a positive torus number (genus) (greater than 0) and whose composition is that of polygons.

example:

Scale Invariance: two or more objects that are homomorphs independently of scale

example:

Scale Variance: two or more objects that are heteromorphs with scale

example:

Structural component: a symmetry operation on topological structures

example:

Structure:

example:

Symmetry:

example:

Symmetry group:

example:

Symmetry number:

example:

Taxonomy: the classification of objects based on shared properties

example:

Topological analog: The corresponding mathematical structure to it physical counterpart

example: