Pentagonal and trigonal quasilattices and their approximants

Abstract

Abstract The Strip Projection Method is used to generate pentagonal and trigonal 2-dimensional quasilattices as rational approximants to the icosahedral quasilattice. Further, 3-dimensionally periodic structures are generated as rational approximants to these 2-dimensional quasilattices. A simplified approach based on uniform distortions of perpendicular space is put forth for the analyses.