Unusual Tilings and Transformations

Jouko Koskinen
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 539–542 Short Papers


I saw a spherical icosidodecahedron in 1956. Later I have had some insights, which have been new for me. The most common cognition has been, that any single answer brings more than one new question. In this paper I am listing some of both. Examples: -- Do rhombic triacontahedra fill the 3D-space twice? -- Concave rhombic triacontahedron as a single 3D-space filler. -- A slim pentagon as a single aperiodic 2D-space filler with 109 different vertices. -- The biggest cuboctahedron inside of an icosidodecahedron seems related with the slim pentagon. -- Pull a dodecahedron to be a tetrahedron. -- Move/turn the faces/edges of any Platonic, Archimedean or Kepler-Poinsot solid or their duals to create any other of those.