// cone9.fe

// Surface Evolver datefile for case 9 of Jean Taylor's classification 
// of possible minimal cones.  See command "gogo" below for evolution
// to absolute minimal surface.

#define alpha (83.80167087*pi/180/2)
#define beta  (58.25684287*pi/180/2)
#define gamma acos(sin(alpha)*sin(2*beta)*cos(2*pi/3)+cos(alpha)*cos(2*beta))
#define theta asin(sin(2*pi/3)*sin(2*beta)/sin(gamma))

vertices
1   sin(alpha)  0 cos(alpha) fixed
2   -sin(alpha) 0 cos(alpha) fixed
3   sin(gamma)*cos(theta) sin(gamma)*sin(theta) cos(gamma) fixed
4  -sin(gamma)*cos(theta) sin(gamma)*sin(theta) cos(gamma) fixed
5  -sin(gamma)*cos(theta) -sin(gamma)*sin(theta) cos(gamma) fixed
6   sin(gamma)*cos(theta) -sin(gamma)*sin(theta) cos(gamma) fixed
7   sin(gamma)*sin(theta) sin(gamma)*cos(theta) -cos(gamma) fixed
8  -sin(gamma)*sin(theta) sin(gamma)*cos(theta) -cos(gamma) fixed
9  -sin(gamma)*sin(theta) -sin(gamma)*cos(theta) -cos(gamma) fixed
10   sin(gamma)*sin(theta) -sin(gamma)*cos(theta) -cos(gamma) fixed
11  0 sin(alpha) -cos(alpha) fixed
12  0 -sin(alpha) -cos(alpha) fixed
13  0 0 0

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

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

read
hessian_normal

// evolution to absolute minimal surface
gogo := { o; // pop central vertex
          refine edge where length > .24 and valence != 2; 
          u;
          g 10; t .05;
          o;  // need to pop again
          V;V;u;V;u;V;
          g 10 ; t .05; V;
          t .05; g 10; w .001;
          g 10; w .001; t .05;
          o;  // need to pop yet again
          V; u; V; u; V;
          g 10; t .05;
          g 10; t .05; w .001;
          g 10; V; u; V; u;
          g 10;
          refine edge where length > .38 and valence != 2;          
          u;u;V;u; g 10;
          hessian_seek; t .05; w .001; g 10 ; hessian_seek;
          w .001; V; hessian_seek;
          r; g 10; hessian_seek; hessian; hessian;
          w .001; u; u; V; g 10; hessian_seek; hessian; hessian;
        }