Rose window graphs underlying rotary maps

Given natural numbers n≥3n≥3 and 1≤a,r≤n−11≤a,r≤n−1, the rose window graph Rn(a,r)Rn(a,r) is a quartic graph with vertex set {xi∣i∈Zn}∪{yi∣i∈Zn}{xi∣i∈Zn}∪{yi∣i∈Zn} and edge set {{xi,xi+1}∣i∈Zn}∪{{yi,yi+r}∣i∈Zn}∪{{xi,yi}∣i∈Zn}∪{{xi+a,yi}∣i∈Zn}{{xi,xi+1}∣i∈Zn}∪{{yi,yi+r}∣i∈Zn}∪{{xi,yi}∣i∈Zn}∪{{xi+a,yi}∣i∈Zn}. In this paper rotary maps on rose window graphs are considered. In particular, we answer the question posed in [S. Wilson, Rose window graphs, Ars Math. Contemp. 1 (2008), 7–19. http://amc.imfm.si/index.php/amc/issue/view/5] concerning which of these graphs underlie a rotary map.