Playing with the Platonics: A New Class of Polyhedra
Inhaltsverzeichnis
Reference
Walt van Ballegooijen: Playing with the Platonics: A New Class of Polyhedra. In: Bridges 2012. Pages 119–124
DOI
Abstract
Intrigued by the impossibility of making a closed loop of face-to-face connected regular tetrahedra, I wondered how adjustments to the polyhedron could make it loop-able. As a result I have defined a method to construct a whole class of new polyhedra based on the Platonic solids. By exploring this class I found several examples of polyhedra that do make closed loops possible, and sometimes it is possible to build 3D lattices or other regular 3D structures with them. This project was however not a complete analyses of all possibilities, but merely a short study.
Extended Abstract
Bibtex
Used References
[1] J.H. Mason, Can regular tetrahedra be glued together face to face to form a ring?, Mathematical Gazette 56 (397), pages 194–197, 1972
[2] S.K. Stein, The planes obtainable by gluing regular tetrahedra, The Mathematical Monthly 85 (6), pages 477–479, 1978
[3] http://en.wikipedia.org/wiki/Boerdijk-Coxeter_helix, as of May 1, 2012
[4] C.S. Kaplan and G.W. Hart, Symmetrohedra: Polyhedra from Symmetric Placement of Regular Polygons, Bridges Conference Proceedings, pages 21–27, 2001
[5] B.M. Stewart, Adventures Among the Toroids: a study of quasi-convex, aplanar, tunneled orientable polyhedra of positive genus having regular faces with disjoint interiors, revised second edition, 1980
[6] http://www.kabai.hu/gallery/rhombic-structures, as of May 1, 2012
Links
Full Text
http://archive.bridgesmathart.org/2012/bridges2012-119.pdf
