Continuous Transformations of Subdivided Periodic Surfaces: Fid-Bau Portal

Continuous Transformations of Subdivided Periodic Surfaces

Lalvani, Haresh

A unified morphological method for generating subdivisions of periodic surfaces is presented. The surfaces are characterized by symmetry, frequency, and the topology of subdivision. An open-ended hyper-cubic lattice is suggested as the structure space within which the subdivided surfaces can transform continuously from one to another by varying different independent parameters. For the purposes of illustration, eight parameters are specified to demonstrate an 8-dimensional model for the structure space. Additional types of subdivisions, and other geometric or physical parameters encountered in building, extend this space to a higher-dimensional one which acts as a systematic framework for generating a large variety of surface structures and their transformations. Geodesic spheres are special cases within this continuum which includes plane surfaces and the hyperbolic tessellations. An infinite class of semi-regular hyperbolic tessellations analogous to the Archimedean polyhedra and plane tessellations are presented, and higher frequency subdivisions of hyperbolic tessellations are suggested.