Vince asked whether for each rational \( r \) between 2 and 4 there was a planar graph of circular chromatic number \( r \). Moser and Zhu showed that the answer is yes, the first for \( 2 < r < 3 \), the second for \( 3 < r < 4 \). This paper gives another family of planar graphs with circular chromatic number between 2 and 3.