I generated SVG images for all regular star polygons up to 50 sides, specifically {p/q}, q<p/2 and gcd(p,q)=1. It's VERY long for the article, so I put them here for reference. I copied ones up to 20 at List_of_regular_polytopes#Stars. Tom Ruen (talk) 09:35, 22 January 2015 (UTC)[reply]
Here's some star figures (compounds) too, n{p/q} with p=2..16, q=1..p/2, and n*p<32. I colored the edges, but looks like yellow was a poor color choice. Tom Ruen (talk) 10:52, 22 January 2015 (UTC) Digon compounds added in first row. Tom Ruen (talk) 18:56, 31 January 2015 (UTC)[reply]
These star polygons are isogonal (vertex-transitive), all solutions for equal-spaced vertices, p=3..16. They have two edge lengths in general, while some have equal edge lengths and are also regular: t{p/q}={2p/q} for odd(q), and t{p/(2p-q)}={2p/(2p-q)} for odd(2p-q). Tom Ruen (talk) 04:01, 29 January 2015 (UTC)[reply]
Isogonal star polygons as truncations of regular convex polygons
{3}:t2
{4}:t2
{4}:t3 t{4/3}={8/3}
{5}:t2
{5}:t3
{6}:t2
{6}:t3
{6}:t4 t{6/5}={12/5}
{7}:t2
{7}:t3
{7}:t4
{8}:t2
{8}:t3
{8}:t4
{8}:t5 t{8/7}={16/7}
{9}:t2
{9}:t3
{9}:t4
{9}:t5
{10}:t2
{10}:t3
{10}:t4
{10}:t5
{10}:t6 t{10/9}={20/9}
{11}:t2
{11}:t3
{11}:t4
{11}:t5
{11}:t6
{12}:t2
{12}:t3
{12}:t4
{12}:t5
{12}:t6
{12}:t7 t{12/11}={24/11}
{13}:t2
{13}:t3
{13}:t4
{13}:t5
{13}:t6
{13}:t7
{14}:t2
{14}:t3
{14}:t4
{14}:t5
{14}:t6
{14}:t7
{14}:t8 t{14/13}={28/13}
{15}:t2
{15}:t3
{15}:t4
{15}:t5
{15}:t6
{15}:t7
{15}:t8
{16}:t2
{16}:t3
{16}:t4
{16}:t5
{16}:t6
{16}:t7
{16}:t8
{16}:t9 t{16/15}={32/15}
Isogonal star polygons as truncations of star polygons