Motivated by a (layered) folding dissection of a 2-high {10/3}-star to a 4-high {5/2}-star, we identify an infinite class of folding dissections for pseudo-stars for which the dissections are cyclicly hinged. In addition to folding dissections of 2-high to 4-high pseudo-stars, the class includes folding dissections of 2-high to (2h)-high pseudo-stars for any whole number h, as well as folding dissections of (2h)-high to (2h′)-high pseudo-stars where h and h′ are whole numbers such that gcd(h, h′) = 1. The total number of pieces in each of these folding dissections is the sum of the number of points in both stars.