GeometricScene extremely slow or cannot complete

I would like to find instances of the following dodecahedral wheel

generalized to the situation where the red squares become rhombuses.

I tried this using RandomInstance[GeometricScene], but Mathematica could not complete it the way I was trying. I tried simplifying the Geometric Scence to some smaller subset of constraints (eliminating the outer 6 ring of equilateral triangles):

RandomInstance[
GeometricScene[{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r,
s},
{
t1 = Triangle[{a, b, c}],
t2 = Triangle[{a, c, d}],
t3 = Triangle[{a, d, e}],
t4 = Triangle[{a, e, f}],
t5 = Triangle[{a, f, g}],
t6 = Triangle[{a, g, b}],

s1 = Style[Polygon[{b, k, l, c}], Red],
s2 = Style[Polygon[{c, m, n, d}], Red],
s3 = Style[Polygon[{d, o, p, e}], Red],
s4 = Style[Polygon[{e, q, r, f}], Red],
s5 = Style[Polygon[{f, s, h, g}], Red],
s6 = Style[Polygon[{g, i, j, b}], Red],

GeometricAssertion[{t1, t2, t3, t4, t5, t6}, "Equilateral",
"Clockwise"],
GeometricAssertion[{s1, s2, s3, s4, s5, s6}, "Equilateral",
"Clockwise"]
}
]]


but this also couldn't complete.

This even smaller subfigure did complete:

RandomInstance[GeometricScene[{a, b, c, d, k, l, m, n},
{
t1 = Triangle[{a, b, c}],
t2 = Triangle[{a, c, d}],
t9 = Triangle[{c, l, m}],

s1 = Style[Polygon[{b, k, l, c}], Red],
s2 = Style[Polygon[{c, m, n, d}], Red],

GeometricAssertion[{t1, t2, t9}, "Equilateral", "Clockwise"],
GeometricAssertion[{s1, s2}, "Equilateral", "Clockwise"]
}
]]


but was very slow.

This doesn't seem to be such a complicated constraints problem, and so I am wondering if there is a better way to do this with GeometricScene?