A Musical Polyhedron Updated for the 21st Century

Cathleen O'Neil
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 407–410 Short Papers


In the 19th century August Möbius described a musical torus constructed on the chromatic scale illustrated with two-dimensional diagrams. In the 20th century A. Harry Wheeler realized Möbius’s concept in a three-dimensional model. With the availability of 3D printers at the beginning of the 21st century, the construction of this musical polyhedron can be reimagined. The flat-pattern models generated by the 3D model make the underlying geometry more accessible, and the new 3D model brings out sculptural qualities that were not as evident before.