Structural Geometric Topology by Albert P. Carpenter

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These images are to be understood as both  mathematical and molecular models in Structural Geometric Topology  and Molecular Geometric Topology.

The definition being used here for Geometric Topology is: the study of topological objects such as Tori/Handlebodies, Annuli/Sieves, Mobius strips/Structures, Knots and Links that are composed of geometric objects such as points, lines, polygons and polyhedra. By conceiving of the discipline in this way it is possible to construct a wealth of models for study.

These objects are the product of a new methodology for mathematics born of Cognitive Science. In that field, it is known as conceptual blending, but I have systematized it and named the process “Systematic Conceptual Integration”. For an outline of this method please see the Methodology page on this site.

The use of color is intended to elucidate the substructures of the which the objects are built.

For every object there would ideally be an accompanying mathematical data sheet with its name, classification and properties etc. Unfortunately, that is beyond my abilities  at this time. However, included at this site is a sample data sheet that would be filled out for each object in the creation of a topological database. In addition to the mathematical data sheet, some day in the future there will also be a physical data sheet for each object depicting its physical analog.

As for the pointal models, there already exists an extensive study of these objects at: the Please go there to see them.

If you wish to comment on this web page and its content please contact me at

Also see my work at: and

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