  The infinite friezes of positive integers were introduced by Tschabold as a
variation of the classical Conway-Coxeter frieze patterns. These infinite
friezes were further shown be to realizable via triangulations of the infinite
strip by Baur, Parsons and Tschabold. In this paper, we show that the
construction of Baur, Parsons and Tschabold can be slightly adapted in order to
obtain a bijection between the infinite friezes and the so-called admissible
triangulations of the infinite strip with no special marked points on the upper
boundary. As a consequence, we obtain that the infinite friezes with enough
ones are in bijection with the admissible triangulations of the infinity-gon.
