Pieces of Pi? Polyhedra, Orthoschemes and Dihedral Kaleidoscopes

Curtis Palmer
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 625–628


Studying polyhedral forms is essential for mathematicians, architects, scientists, biologists, even artists, and for children it can be a lot of creative fun. This workshop will show that dihedral kaleidoscopes are useful tools for teaching mathematical concepts to a range of age groups. Workshop participants will experience creating a paper orthoscheme (also called: simplex, plug, quantum of shape, symmetry unit) and discover that polyhedra can be understood as products of kaleidoscopic reflections and rotations of such a simplex, see Coxeter [3]. The workshop will conclude with the collective creation of a paper polyhedra out of individualized, i.e. decorated simplexes. This transient sculpture will serve as visceral proof of the polyhedral consequences of symmetry operations.