Rashmi Sunder-Raj

This piece came about from an investigation of rhombus patterns which can be created from portions of regular n-fold rhombus rosettes. In particular this 5-fold pattern is constructed using the shapes which appear in a 60-fold rosette. The central pattern is made of what I would call 5 intersecting curved “2π/60-rhombus worms”. Given an angle θ (here I am only exploring those angles which divide nicely into 2π), a θ-rhombus worm consists of a chain of rhombi with angles (θ,π-θ), (2θ, π-2θ), (3θ,π-3θ),...,ending in either (π-θ,θ) or (π-θ/2,θ/2) depending on whether or not θ divides π. The rhombi are hinged so that all lie on one side of a very bendy spine. If we let n=2π/θ, the curved form can be rotated to form an n-fold rhombus rosette.

This is a pattern of edge-touching regular dodecagons arranged to suggest irregular pentagonal tiles forming a Cairo Tiling. I have been exploring how various regular polygons can give rise to the formation of irregular pentagons with different angles. Here, each “tile” approximates a 120°-90°-120°-90°-120° pentagon, giving the dual of the snub square tiling (3.3.4.3.4). The arrangement and colouring of the dodecagons hint at the location of the vertices of the triangles and squares in 3.3.4.3.4. I hope to eventually convert this pattern to physical form using either a type of bead crochet, or linked jump rings.