Geometric Factors and the Well Dressed Solids of Archimedes

Stan Spencer
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 167–174 Regular Papers


I have shown, in previous papers, that any regular polygon with n sides can be dissected into a set of isosceles triangles. These same triangles can be used to create other regular polygons with m sides provided that m is a factor of n. An enlarged version of each triangle can be created using the same isosceles triangles. In this paper I have shown how these ideas can be used to create Archimedean solids from the dissection of a single polygon. Well Dressing is a tradition in many small villages in the Pennine areas of rural England in which village wells are decorated with mosaics made from natural materials. The polygons for these solids can be in the form of an irregular tiling or a fractal. In the case of a fractal pattern I have used decorations from the Well Dressing at Hodthorpe Primary School as an inspiration for for colour choices and a source of images for decorating Archimedian solids