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?

Thanks for any help you might provide.