Polyhedral Transformation: Explosion-Implosion

Robert McDermott
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 481–488


Polyhedral transformation software continuously produced polyhedron. In other words, for different inputs, a different polyhedron was output. For some, the output was a Platonic or Archimedean polyhedron. The transformation was modeled as a fundamental region of a polyhedron, and when polygons from a fundamental region were combined with symmetry transformations of reflections and rotations, a complete polyhedron was formed. These complete polyhedron originated from the tetrahedral, octahedral, and icosahedral families. With the use of animation, the polyhedron were transformed smoothly and continuously from one polyhedron to another. For example, an icosahedron was transformed into a dodecahedron.