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stellated icosagedron

a = (1+sqrt(5))/2;
    
b = [1, 0, a]; // b through m are the vertices of an icosahedron
c = [-1, 0, a]; // n through v are the vertices of the stellation
d = [1, 0, -a]; // find the equations of each plane, put the coefficients
e = [-1, 0, -a]; // of 3 of them into a matrix, RREF, that is
f = [0, a, -1]; // the vertex of the stellation
g = [0, -a, -1];
h = [0, a, 1];
i = [0, -a, 1];
j = [-a, -1, 0];
k = [a, -1, 0];
l = [-a, 1, 0];
m = [a, 1, 0];
n = [0, 2.618033989, 0];
o = [1.170820393, 2.618033989, -1.170820393];
p = [.8090169944, 1.309016994, -2.118033989];
q = [2.118033989, -.8090169944, 1.3090169944];
r = [3.065247584, -.4472135955, 0];
s = [2.118033989, -.8090169944, -1.309016994];
t = [-2.618033989, 0, 0];
u = [-2.618033989, -1.170820393, 1.170820393];
v = [-1.309016994, -2.118033989, .8090169944];
    

// the paths come in pairs to connect the vertices

paths = [
         h, c, c, b, b, h, f, l, l, j, j, i, i, k, k, m, m, f,
     d, e, e, g, g, d, h, m, h, f, h, l, c, l, c, j, c, i,
     b, i, b, k, b, m, h, m, h, f, h, l, d, k, d, m, d, f,
     e, f, e, l, e, j, g, j, g, i, g, k,
     h, n, n, o, m, o, o, p, d, p, p, e, e, t, t, n, t, u, u, c,
     u, v, v, g, v, q, g, s, s, r, r, q, b, q, s, d, r, m
];


rotate([20.90515746, 0, 0]) // lays the shape flat
{
     for(n=[0:51]) // connects each pair of paths
     {
         vert_1 = paths[2*n];
         vert_2 = paths[2*n+1];
         hull()
         {
                 translate([vert_1[0], vert_1[1], vert_1[2]])
                 {
                     sphere($fn=100, .2, true);
                 }
                 translate([vert_2[0], vert_2[1], vert_2[2]])
                 {
                     sphere($fn=100, .2, true);
                 }
         }
     }
}