id: 06302312
dt: j
an: 2015d.00814
au: Ehrenborg, Richard
ti: Hamiltonian cycles on Archimedean solids are twisting free.
so: Am. Math. Mon. 121, No. 2, 158-161 (2014).
py: 2014
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: K35 G95
ut: Archimedean solids; Hamiltonian tour
ci:
li: doi:10.4169/amer.math.monthly.121.02.158
ab: The dual graph of an Archimedean solid is a graph with a vertex for each
(two-dimensional) face of the solid. Two vertices are adjacent in the
dual graph if the corresponding faces intersect along an edge of the
solid. A Hamiltonian cycle on an Archimedean solid is defined as a
Hamiltonian cycle in its dual graph, and hence can be viewed as a walk
along the faces of the solid so that each face is visited once and such
that the walk begins and ends on the same face. The main result of this
paper shows that a Hamiltonian cycle on an Archimedean solid is free of
twisting in the sense that when the cycle returns to its initial face,
that face has the same orientation as it did at the beginning of the
tour.
rv: Steven Klee (Seattle)