Star polygons can also be isotoxal, labeled as \{(n/q)_\alpha\}, with q \le n - 1 and with the greatest common divisor \gcd(n,q) = 1, where q is the turning number or density.Tilings and Patterns, Branko Gruenbaum, G.C. Shephard, 1987. 2.5 Tilings using star polygons, pp. 82-85. Concave inner vertices can be defined for q < n/2. If D = \gcd(n,q) \ge 2, then \{(n/q)_\alpha\} = \{(Dm/Dp)_\alpha\} is "reduced" to a compound D \{(m/p)_\alpha\} of D rotated copies of \{(m/p)_\alpha\}.
