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- W1523288485 abstract "In this series of two papers we construct quasi reg ular polyhedra and their duals which are similar to the Catalan solids. The group elements as well as the vertices of the p olyhedra are represented in terms of quaternions. I n the present paper, we discuss the quasi regular polygons (isogonal and is otoxal polygons) using 2D Coxeter diagrams. In part icular, we discuss the isogonal hexagons, octagons and decagons derived from 2D Coxeter diagrams and obtain aperiodic tilings of the plane with the isogonal polygons along with the regular polygo ns. We point out that one type of aperiodic tiling of the plane with regular and isogonal hexagons may represent a state of grapheme, where one carbon atom is bound to thr ee neighboring carbons with two single bonds and one double bond. We also show how the plane can be tiled with two ti les; one of them is the isotoxal polygon, dual of the isogonal polygon. A general method is employed for the constructions of the regular and quasi regular prisms and their duals in 3D dimensio ns with the use of 3D Coxeter diagrams." @default.
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- W1523288485 date "2011-07-26" @default.
- W1523288485 modified "2023-09-27" @default.
- W1523288485 title "QUASI REGULAR POLYHEDRA AND THEIR DUALS WITH COXETER SYMMETRIES REPRESENTED BY QUATERNIONS - II" @default.
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