Harnessing the properties of a three-dimensional constant-volume strain and the combination and complexity of the polymorphism of amalgamation polytopes and tessellation, the author has derived at a spectacular generation of some 200 genres of fabric that presents an exclusive range of some 6,000 unique design of digital lace patterns, exotic batiks, Oriental silk and more. This paper presents the inherent properties and beauty of the results produced by these strained axes when combined with a whole slew of demiregular tessellation. It presents and demonstrates an orthography of the overlapping demiregular tessellation that spawns polytope vertex whereby the results of more than one transitivity class of vertices lead to an infinite number of possible tessellations.

Keywords: tessellation, demiregular tessellation, polygons, polyhedra, polytopes, amalgamation, polymorphism, automorphism, finite strain, mathematics, art, fabrics