Inside and Outside the Rhombic Hexecontahedron
Inhaltsverzeichnis
Reference
Sándor Kabai: Inside and Outside the Rhombic Hexecontahedron. In: Bridges 2011. Pages 387–394
DOI
Abstract
The rhombic hexecontahedron is a twenty-pointed star polyhedron that is bounded by sixty golden rhombi. It can be understood as a stellation of its relative, the Keplerian rhombic triacontahedron, or as the assembly as twenty prolate golden rhombohedra. This study investigates these relationships and the possible structures that can be created by dissecting and recombining parts of these forms. Many possible structures are introduced with the help of Wolfram Mathematica graphics, the Zometool construction set, and the author's own StyroBlock modeling system, see www.kabai.hu).
Extended Abstract
Bibtex
Used References
[1] Unkelbach, H. Die kantensymmetrischen, gleichkantigen Polyeder. Deutsche Math. 5, 1940.
[2] http://www.georgehart.com/virtual-polyhedra/five-cube-intersection.html
[3] Guyot, P. News on Five-Fold Symmetry. Nature 326, 640-641, 1987.
[4] http://en.wikipedia.org/wiki/Quasicrystal
[5] Á. Csanády et al, Proceedings of the 8th ILMC(1987) 486
[6] H. U. NissenR.Wessicken,C. Beelii and Á. Csanády, Phil. Mag. 57, 1988,587
[7] Kabai S., Bérczi Sz. Rhombic Structures, UNICONSTANT, 2009
[8] http://demonstrations.wolfram.com/index.html
[9] Kabai S., Mathematical Graphics with the use of Mathematica, UNICONSTANT, 2002
[10] http://matematika.fe.uni-lj.si/people/izidor/homepage/
[11] Grünbaum B., A new rhombic hexecontahedron, Geombinatorics 6(1996), 15 -18.
[12] Longuet-Higgins, M.S., On the use of symmetry, in Hargittai, I., editor, Symmetry 2000.
[13] Hart, G., Procedural Generation of Sculptural Forms, Bridges 2008.
[14] http://www.wolframalpha.com/
[15] Grünbaum, B. "A New Rhombic Hexecontahedron--Once More." Geombinatorics, 6, 55-59, 1996.
[16] Messer, P. W. Stellations of the Rhombic Triacontahedron. Structural Topology 21, 25-46, 1995.
Links
Full Text
http://archive.bridgesmathart.org/2011/bridges2011-387.pdf
