Spelunking Adventure VI: An Equal Tempered Icosahedral Scale

Curtis Palmer
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 557–560 Short Papers


With 3D Computer Aided Design I have divided 12 unit radius icosahedral polyhedra into sets of ’symmetry units’ represented in software as blocks containing graphic elements. These 12 polyhedral systems’ radii are assigned a length to match a musical note’s position in a chromatic scale. Combining these polyhedral system notes creates and names a chord consisting of concentric polyhedra (matroyska domes). To paint these objects I use a recursive self texturing technique. With 3D path and turntable animation tools I create movies: visual songs or intonations that document what a virtual camera sees as it transits “In, Out and Around” this menagerie of painted forms.