// cone8.fe

// Surface Evolver datafile for case 8 of Jean Taylor's classification 
// of possible minimal cones.
// See command "gogo" below for evolution to absolute minimal surface.

#define beta (asin(sqrt(2)/sqrt(3)))
#define gamma (asin( sqrt((sqrt(sqrt(2)) - 1)^2/6 + (2-sqrt(2))^2/12) ) )
#define h1  cos(beta)
#define r1  sin(beta)
#define h2  cos(beta + 2*gamma)
#define r2  sin(beta + 2*gamma)
#define a   sqrt(0.5)

vertices
1  r1 0 h1 fixed
2   0 r1 h1 fixed
3  -r1 0 h1 fixed
4   0 -r1 h1 fixed
5  r2 0 h2 fixed
6  0 r2 h2 fixed
7  -r2 0 h2 fixed
8  0 -r2 h2 fixed
9  a*r2 a*r2 -h2 fixed
10 -a*r2 a*r2 -h2 fixed
11 -a*r2 -a*r2 -h2 fixed
12 a*r2 -a*r2 -h2 fixed
13  a*r1 a*r1 -h1 fixed
14 -a*r1 a*r1 -h1 fixed
15 -a*r1 -a*r1 -h1 fixed
16 a*r1 -a*r1 -h1 fixed
17  0 0 0

edges
1  1 2 fixed
2  2 3 fixed 
3  3 4 fixed
4  4 1 fixed
5  1 5 fixed
6  2 6 fixed
7  3 7 fixed
8  4 8 fixed
9  5 9 fixed
10  9 6 fixed
11  6 10 fixed
12  10 7 fixed
13  7 11 fixed
14  11 8 fixed
15  8 12 fixed
16  12 5 fixed
17  9 13 fixed
18  10 14 fixed
19  11 15 fixed
20  12 16 fixed
21  13 14 fixed
22  14 15 fixed
23  15 16 fixed
24  16 13 fixed
25  1 17
26  2 17
27  3 17
28  4 17
29  5 17
30  6 17
31  7 17
32  8 17
33  9 17
34  10 17
35  11 17
36  12 17
37  13 17
38  14 17
39  15 17
40  16 17

faces
1   1 26 -25
2   2 27 -26
3   3 28 -27
4   4 25 -28
5   5 29 -25
6   6 30 -26
7   7 31 -27
8   8 32 -28
9   9 33 -29
10  10 30 -33
11  11 34 -30
12  12 31 -34
13  13 35 -31
14  14 32 -35
15  15 36 -32
16  16 29 -36
17  17 37 -33
18  18 38 -34
19  19 39 -35
20  20 40 -36
21  21 38 -37
22  22 39 -38
23  23 40 -39
24  24 37 -40

read
hessian_normal

// command to pop central vertex and evolver
gogo := { o;  // pop central vertex
          refine edge where valence != 2;
          g 10; t .06; g 10; u; w .001; g 10; t .06; g 10;
          V; g 20; V; V; g 10; hessian_seek; hessian_seek;
          t .06; V;V;V;V; hessian_seek; r; u;u;V;u; g 10;
          hessian_seek; r; u; u; g 5; hessian_seek;
          hessian_seek; hessian;
        }