// cone10.fe

// Surface Evolver datafile for case 10 of Jean Taylor's 
// classification of possible minimal cones.
// See "gogo" command at end for evolution to absolute minimal surface.

#define alpha asin(1/sqrt(3))
#define beta  asin(sqrt((3-sqrt(6))/6))
#define gamma asin((sqrt(3)-sqrt(2))/2/sqrt(3))
#define r1 sin(2*beta)
#define h1 cos(2*beta)

vertices
1  0 0 1 fixed
2  r1 0 h1 fixed
3  r1*cos(2*pi/3) r1*sin(2*pi/3) h1 fixed
4  r1*cos(4*pi/3) r1*sin(4*pi/3) h1 fixed
5  cos(pi/3-gamma) sin(pi/3-gamma) 0 fixed
6  cos(pi/3+gamma) sin(pi/3+gamma) 0 fixed
7  cos(pi-gamma) sin(pi-gamma) 0 fixed
8  cos(pi+gamma) sin(pi+gamma) 0 fixed
9  cos(5*pi/3-gamma) sin(5*pi/3-gamma) 0 fixed
10  cos(5*pi/3+gamma) sin(5*pi/3+gamma) 0 fixed
11  r1 0 -h1 fixed
12  r1*cos(2*pi/3) r1*sin(2*pi/3) -h1 fixed
13  r1*cos(4*pi/3) r1*sin(4*pi/3) -h1 fixed
14  0 0 -1 fixed
15  0 0 0

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

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

read
hessian_normal

// Command for evolution to absolute minimal surface
gogo := { o;  // pop central vertex
          refine edge where length > .19 and valence != 2;
          u;u; g 10; t .05; V; g 10; t .05;
          o;  // need to pop again
          V; V; u; u; g 10 ; t .05; g 10; V; g 10;
          t .05; w .001; g 10; t .05; g 10;
          hessian_seek; V; t .05; hessian_seek; hessian_seek;
          refine edge where valence != 2 and length > .35;
          V; g 10; hessian_seek;
          r; g 10 ; u; u; g 10;
          hessian_seek; hessian; hessian;
          u;V;u;V; g 10; hessian_seek; hessian;
        }