// dcell.fe // Surface Evolver datafile for fundamental region for Schwartz' D minimal surface // 1/24 of cube // Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu /* Commands: gogo - typical evolution showcube - display cubic unit cell showfour - show four cubic unit cells showrhombic - show rhombic dodecahedron unit cell transforms off - show just single fundamental region setcolor - to color one side yellow, as in my web page. To turn off showing all the edges in the graphics display, hit the "e" key in the graphics window. */ symmetric_content parameter fudge = 1/3 constraint 1 // top formula: x + z = 2 content: c1: fudge*(y+1) c2: fudge*(1-x) c3: 0 constraint 2 // right side formula: y - x = 0 constraint 3 // left side formula -x-y = 0 constraint 4 // front formula: x - z = 0 view_transform_generators 8 0,1,0,0 1,0,0,0 0,0,1,0 0,0,0,1 // a: x,y swap 0,-1,0,0 -1,0,0,0 0,0,1,0 0,0,0,1 // b: x+y=0 mirror 0,0,1,0 0,1,0,0 1,0,0,0 0,0,0,1 // c: x,z swap swap_colors 1 0 0 2 , 0 1 0 0, 0 0 1 0, 0 0 0 1 // d: x translation by 2 swap_colors 1 0 0 0 , 0 1 0 2, 0 0 1 0, 0 0 0 1 // e: y translation by 2 swap_colors 1 0 0 0 , 0 1 0 0, 0 0 1 2, 0 0 0 1 // f: z translation by 2 swap_colors 1 0 0 0, 0 -1 0 0, 0 0 -1 2, 0 0 0 1 // g: C2 rotation about x axis swap_colors -1 0 0 0, 0 1 0 0, 0 0 -1 2, 0 0 0 1 // h: C2 rotation about y axis vertices 2 1 0 1 fixed 3 .5 .5 .5 constraints 2,4 4 0 0 1 fixed 5 0 0 0 fixed bare // for tetrahedron outline 6 0 0 1 fixed bare 7 1 -1 1 fixed bare 8 1 1 1 fixed bare edges 2 2 3 constraint 4 3 3 4 constraint 2 4 4 2 fixed 5 5 6 fixed bare no_refine // for tetrahedron display 6 5 7 fixed bare no_refine 7 5 8 fixed bare no_refine 8 6 7 fixed bare no_refine 9 6 8 fixed bare no_refine 10 7 8 fixed bare no_refine facets 1 2 3 4 bodies 1 1 volume 1/12 read hessian_normal // command to show full cell in rhombic dodecahedron showrhombic := { transform_expr "abcabcg"; transforms on; set edge color black; set edge color clear where bare and original != 7 and original != 6; show_trans "R"; } // command to show full cell in cube showcube := { transform_expr "abcabc"; transforms on; set edge color black; set edge color clear where bare and original != 9; show_trans "R"; } // command to show four full cells showfour := { transform_expr "efabcabc"; transforms on; set edge color clear where bare; show_trans "R"; } // command to show eight full cells showeight := { transform_expr "defabcabc"; transforms on; set edge color clear where bare; show_trans "R"; } // Alternate unit cell, more suitable for 3D printing // command to show full cell in cube showcube_alt := { transform_expr "hgaca"; transforms on; set edge color black; set edge color clear where bare; show_trans "R"; } // command to show four full cells showfour_alt := { transform_expr "efhgaca"; transforms on; set edge color clear where bare; show_trans "R"; } // command to show eight full cells showeight_alt := { transform_expr "defhgaca"; transforms on; set edge color clear where bare; show_trans "R"; } // Alternate unit cell, more suitable for 3D printing setcolor := { set facet backcolor yellow } // To show just one fundamental region, do "transforms off". // To show tetrahedron outline again, do "show edges". // A typical evolution gogo := { g 5; r; g 5; r; g 5; r; g 10; r; g 10; hessian; hessian; } /* dcell commands: gogo - typical evolution showcube - display cubic unit cell showfour - show four cubic unit cells showeight - show eight cubic unit cells showrhombic - show rhombic dodecahedron unit cell transforms off - show just single fundamental region setcolor - to color one side yellow, as in my web page. */