Ribbon tilings from spherical ones (Q1815258)

The author shows that the classification of tilings of a (pinched) ribbon being equivariant with respect to one of the seven frieze groups can be obtained from the classification of certain equivariant spherical tilings. It is an application of the observation made in a paper of the reviewer and the author [Geom. Dedicata 60, No. 1, 89-106 (1996; Zbl 0852.52012)] that there is a canonical correspondence between the sets of tilings equivariant with respect to \(\Gamma_1\) and \(\Gamma_2\), respectively, if the two-dimensional orbifolds associated with \(\Gamma_1\) and \(\Gamma_2\) are of the same form. It may be noteworthy that this result has found applications in the industrial design of tyres.