id: 06101275
dt: j
an: 2013b.00007
au: Nishiyama, Yutaka
ti: The Sepak Takraw ball puzzle.
so: Int. J. Pure Appl. Math. 79, No. 2, 281-292 (2012).
py: 2012
pu: Academic Publications, Sofia
la: EN
cc: A20 G40 M90 M60
ut: Euler’s polyhedron formula; regular polyhedron; semi-regular polyhedron;
truncated icosahedron; soccer ball; fullerene $\mathrm{C}_{60}$
molecule; Sepak Takraw
ci:
li: http://www.ijpam.eu/contents/2012-79-2/9/index.html
ab: Motivated by the observation that Thailandian ball game Sepak Takraw uses a
ball in the shape of a truncated icosahedron, the author of the paper
under review sets out to describe a method for constructing such a
solid from simple packing tape, and to record certain observations
regarding this solid and other solids. He observes that the truncated
icosahedron is also the shape of an ordinary soccer ball and the shape
of the fullerene $\mathrm{C}_{60}$ molecule made famous by the award of
the Nobel prize in chemistry in 1996 to H. Kroto, R. Curl, and R.
Smalley. He then moves on to prove Euler’s polyhedron formula and
that there are only five regular polyhedra, and then he calculates the
number of pentagonal and hexagonal faces of this solid and certain
relations between its radius and the side lengths of its faces. Most of
the material in the paper is contained in the first course of
elementary Euclidean geometry offered by universities such as in the
causes of the reviewer, and thus the paper can be used as supplementary
reading in such a course.
rv: Mowaffaq Hajja (Irbid)