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Copy pathPentagonal_Hexec.scad
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Pentagonal_Hexec.scad
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//Pentagonal Hexecontahedron
phi = (1+sqrt(5))/2;
a = sqrt(phi-5/27);
b = pow((phi + a)/2,1/3);
c = pow((phi - a)/2,1/3);
x = b + c;
C0 = phi * sqrt(3 - pow(x,2)) / 2;
C1 = phi * sqrt((x - 1 - (1/x)) * phi) / (2 * x);
C2 = phi * sqrt((x - 1 - (1/x)) * phi) / 2;
C3 = pow(x,2) * phi * sqrt(3 - pow(x,2)) / 2;
C4 = phi * sqrt(1 - x + (phi + 1) / x) / 2;
C5 = sqrt(x * (x + phi) + 1) / (2 * x);
C6 = sqrt((x + 2) * phi + 2) / (2 * x);
C7 = sqrt(-pow(x,2) * (phi + 2) + x * (3 * phi + 1) + 4) / 2;
C8 = (phi + 1) * sqrt(1 + (1/x)) / (2 * x);
C9 = sqrt(3 * phi + 2 - 2 * x + (3/x)) / 2;
C10 = sqrt(pow(x,2)*(225*phi + 392) + x*(670*phi + 249) + (157*phi + 470))/62;
C11 = phi * sqrt(x * (x + phi) + 1) / (2 * x);
C12 = phi * sqrt(pow(x,2) + x + phi + 1) / (2 * x);
C13 = phi * sqrt(pow(x,2) + 2 * x * phi + 2) / (2 * x);
C14 = sqrt(pow(x,2) * (2 * phi + 1) - phi) / 2;
C15 = phi * sqrt(pow(x,2) + x) / 2;
C16 = pow(phi,3) * sqrt(x * (x + phi) + 1) / (2 * pow(x,2));
C17 = sqrt(pow(x,2)*(842*phi + 617) + x*(1589*phi + 919) + (784*phi + 627))/62;
C18 = pow(phi,2) * sqrt(x * (x + phi) + 1) / (2 * x);
C19 = phi * sqrt(x * (x + phi) + 1) / 2;
font = "Liberation Sans";
letter_size = 5;
letter_height = 0.75;
lsx = 5.4;
gr = (1 + sqrt(5))/2;
// rotate([35.88,0,0])
scale(1.25)
union ()
{
scale(12)
polyhedron(Pentagonal_Hexec_cords, Pentagonal_Hexec_faces);
decorate_15();
}
Pentagonal_Hexec_cords = [
[ C0, C1, C19],
[ C0, -C1, -C19],
[ -C0, -C1, C19],
[ -C0, C1, -C19],
[ C19, C0, C1],
[ C19, -C0, -C1],
[-C19, -C0, C1],
[-C19, C0, -C1],
[ C1, C19, C0],
[ C1, -C19, -C0],
[ -C1, -C19, C0],
[ -C1, C19, -C0],
[ 0.0, C5, C18],
[ 0.0, C5, -C18],
[ 0.0, -C5, C18],
[ 0.0, -C5, -C18],
[ C18, 0.0, C5],
[ C18, 0.0, -C5],
[-C18, 0.0, C5],
[-C18, 0.0, -C5],
[ C5, C18, 0.0],
[ C5, -C18, 0.0],
[ -C5, C18, 0.0],
[ -C5, -C18, 0.0],
[ C10, 0.0, C17],
[ C10, 0.0, -C17],
[-C10, 0.0, C17],
[-C10, 0.0, -C17],
[ C17, C10, 0.0],
[ C17, -C10, 0.0],
[-C17, C10, 0.0],
[-C17, -C10, 0.0],
[ 0.0, C17, C10],
[ 0.0, C17, -C10],
[ 0.0, -C17, C10],
[ 0.0, -C17, -C10],
[ C3, -C6, C16],
[ C3, C6, -C16],
[ -C3, C6, C16],
[ -C3, -C6, -C16],
[ C16, -C3, C6],
[ C16, C3, -C6],
[-C16, C3, C6],
[-C16, -C3, -C6],
[ C6, -C16, C3],
[ C6, C16, -C3],
[ -C6, C16, C3],
[ -C6, -C16, -C3],
[ C2, C9, C15],
[ C2, -C9, -C15],
[ -C2, -C9, C15],
[ -C2, C9, -C15],
[ C15, C2, C9],
[ C15, -C2, -C9],
[-C15, -C2, C9],
[-C15, C2, -C9],
[ C9, C15, C2],
[ C9, -C15, -C2],
[ -C9, -C15, C2],
[ -C9, C15, -C2],
[ C7, C8, C14],
[ C7, -C8, -C14],
[ -C7, -C8, C14],
[ -C7, C8, -C14],
[ C14, C7, C8],
[ C14, -C7, -C8],
[-C14, -C7, C8],
[-C14, C7, -C8],
[ C8, C14, C7],
[ C8, -C14, -C7],
[ -C8, -C14, C7],
[ -C8, C14, -C7],
[ C4, -C12, C13],
[ C4, C12, -C13],
[ -C4, C12, C13],
[ -C4, -C12, -C13],
[ C13, -C4, C12],
[ C13, C4, -C12],
[-C13, C4, C12],
[-C13, -C4, -C12],
[ C12, -C13, C4],
[ C12, C13, -C4],
[-C12, C13, C4],
[-C12, -C13, -C4],
[ C11, C11, C11],
[ C11, C11, -C11],
[ C11, -C11, C11],
[ C11, -C11, -C11],
[-C11, C11, C11],
[-C11, C11, -C11],
[-C11, -C11, C11],
[-C11, -C11, -C11]
];
Pentagonal_Hexec_faces = [
[ 24, 0, 2, 14, 36 ],
[ 24, 36, 72, 86, 76 ],
[ 24, 76, 40, 16, 52 ],
[ 24, 52, 64, 84, 60 ],
[ 24, 60, 48, 12, 0 ],
[ 25, 1, 3, 13, 37 ],
[ 25, 37, 73, 85, 77 ],
[ 25, 77, 41, 17, 53 ],
[ 25, 53, 65, 87, 61 ],
[ 25, 61, 49, 15, 1 ],
[ 26, 2, 0, 12, 38 ],
[ 26, 38, 74, 88, 78 ],
[ 26, 78, 42, 18, 54 ],
[ 26, 54, 66, 90, 62 ],
[ 26, 62, 50, 14, 2 ],
[ 27, 3, 1, 15, 39 ],
[ 27, 39, 75, 91, 79 ],
[ 27, 79, 43, 19, 55 ],
[ 27, 55, 67, 89, 63 ],
[ 27, 63, 51, 13, 3 ],
[ 28, 4, 5, 17, 41 ],
[ 28, 41, 77, 85, 81 ],
[ 28, 81, 45, 20, 56 ],
[ 28, 56, 68, 84, 64 ],
[ 28, 64, 52, 16, 4 ],
[ 29, 5, 4, 16, 40 ],
[ 29, 40, 76, 86, 80 ],
[ 29, 80, 44, 21, 57 ],
[ 29, 57, 69, 87, 65 ],
[ 29, 65, 53, 17, 5 ],
[ 30, 7, 6, 18, 42 ],
[ 30, 42, 78, 88, 82 ],
[ 30, 82, 46, 22, 59 ],
[ 30, 59, 71, 89, 67 ],
[ 30, 67, 55, 19, 7 ],
[ 31, 6, 7, 19, 43 ],
[ 31, 43, 79, 91, 83 ],
[ 31, 83, 47, 23, 58 ],
[ 31, 58, 70, 90, 66 ],
[ 31, 66, 54, 18, 6 ],
[ 32, 8, 11, 22, 46 ],
[ 32, 46, 82, 88, 74 ],
[ 32, 74, 38, 12, 48 ],
[ 32, 48, 60, 84, 68 ],
[ 32, 68, 56, 20, 8 ],
[ 33, 11, 8, 20, 45 ],
[ 33, 45, 81, 85, 73 ],
[ 33, 73, 37, 13, 51 ],
[ 33, 51, 63, 89, 71 ],
[ 33, 71, 59, 22, 11 ],
[ 34, 10, 9, 21, 44 ],
[ 34, 44, 80, 86, 72 ],
[ 34, 72, 36, 14, 50 ],
[ 34, 50, 62, 90, 70 ],
[ 34, 70, 58, 23, 10 ],
[ 35, 9, 10, 23, 47 ],
[ 35, 47, 83, 91, 75 ],
[ 35, 75, 39, 15, 49 ],
[ 35, 49, 61, 87, 69 ],
[ 35, 69, 57, 21, 9 ]
];
module decorate_15()
{
decorate ( 2*gr, -gr*gr, gr ,"1",0,2,180);
decorate ( 1, -gr*gr*gr, 1 ,"1",0,-3,0);
decorate ( gr*gr*gr, -1, 1 ,"1",3,2,-225);
decorate ( gr*gr*gr, 1, -1 ,"1",-1.5,-2,-45);
decorate ( gr*gr*gr, -1, -1 ,"2",2,-1.5,45);
decorate ( gr*gr*gr, 1, 1 ,"2",-3,2,225);
decorate ( 2*gr, -gr*gr, -gr ,"2",-1,-2,-30);
decorate ( (2+gr), 0, -gr*gr ,"2",0,3,180);
decorate ( gr*gr, -(2+gr), 0 ,"3",0,-3,0);
decorate ( gr, -2*gr, gr*gr ,"3",2,-1,90);
decorate ( 1, gr*gr*gr, 1 ,"3",-2,-2,-45);
decorate ( -1, gr*gr*gr, -1 ,"3",2,1,135);
decorate ( -1, gr*gr*gr, 1 ,"4",2,-2,45);
decorate ( -2*gr, gr*gr, gr ,"4",0,3,180);
decorate ( 0, gr*gr, (2+gr) ,"4",0,3,180);
decorate ( gr*gr, gr, 2*gr ,"4",2,-2,45);
decorate ( -gr, 2*gr, gr*gr ,"5",3,0,90);
decorate ( -gr*gr, (2+gr), 0 ,"5",-2,0,-90);
decorate ( gr, 2*gr, gr*gr ,"5",-2,0,-90);
decorate ( gr*gr, (2+gr), 0 ,"5",3,0,90);
decorate ( -gr*gr*gr, -1, -1 ,"6",-3,-2,-45);
decorate ( -gr*gr, -gr, -2*gr ,"6",3,1,120);
decorate ( -2*gr, -gr*gr, -gr ,"6",2,-3,30);
decorate ( -1, -gr*gr*gr, -1 ,"6",-2,2,225);
decorate ( 0, -gr*gr, (2+gr) ,"7",0,3,180);
decorate ( gr*gr, -gr, 2*gr ,"7",-1.5,-1.5,-60);
decorate ( -1, -gr*gr*gr, 1 ,"7",-2,-2,-45);
decorate ( 1, -gr*gr*gr, -1 ,"7",0,3,150);
decorate ( -gr, -2*gr, gr*gr ,"8",-2,0,-90);
decorate ( -gr*gr, -(2+gr), 0 ,"8",2,0,90);
decorate ( -(2+gr), 0, gr*gr ,"8",0,-3,0);
decorate ( -2*gr, -gr*gr, gr ,"8",1,3,-210);
decorate ( -1, 1, gr*gr*gr ,"9",-3,1,-120);
decorate ( 1, -1, gr*gr*gr ,"9",-2,-1,-90);
decorate ( -1, -1, gr*gr*gr ,"9",2,0,90);
decorate ( 1, 1, gr*gr*gr ,"9",3,-1,90);
decorate ( -gr*gr, gr, 2*gr ,"10",-2,-3,-30);
decorate ( -gr*gr*gr, 1, 1 ,"10",3,1,120);
decorate ( -gr*gr, -gr, 2*gr ,"10",1,-3,30);
decorate ( -gr*gr*gr, -1, 1 ,"10",-3,2,-120);
decorate ( -gr*gr*gr, 1, -1 ,"11",1,-2,45);
decorate ( -gr*gr, gr, -2*gr ,"11",-3,2,-120);
decorate ( -2*gr, gr*gr, -gr ,"11",0,-3,-20);
decorate ( -(2+gr), 0, -gr*gr ,"11",0,3,180);
decorate ( gr, 2*gr, -gr*gr ,"12",-2,1,-90);
decorate ( 1, 1, -gr*gr*gr ,"12",3,0,90);
decorate ( 1, gr*gr*gr, -1 ,"12",-3,1,-120);
decorate ( 2*gr, gr*gr, -gr ,"12",-1,-2,0);
decorate ( 0, gr*gr, -(2+gr),"13",0,-2,0);
decorate ( gr*gr, gr, -2*gr ,"13",2,1,135);
decorate ( -gr, 2*gr, -gr*gr ,"13",3,0,90);
decorate ( -1, 1, -gr*gr*gr ,"13",-3,-1,-60);
decorate ( 2*gr, gr*gr, gr ,"14",0,3,180);
decorate ( (2+gr), 0, gr*gr ,"14",0,-3,0);
decorate ( 0, -gr*gr, -(2+gr) ,"14",0,-3,0);
decorate ( gr*gr, -gr, -2*gr ,"14",-1,2,210);
decorate ( -gr, -2*gr, -gr*gr ,"15",-3,0,-90);
decorate ( -1, -1, -gr*gr*gr ,"15",3,0,90);
decorate ( gr, -2*gr, -gr*gr ,"15",3,0,90);
decorate ( 1, -1, -gr*gr*gr ,"15",-2,0,-90);
}
module decorate (x2,y2,z2,char,x3,y3,ang)
{
translate(v=[lsx*x2,lsx*y2,lsx*z2])
rotate(a = -[acos(z2/sqrt(x2*x2+y2*y2+z2*z2)), 0, atan2(x2, y2)])
linear_extrude(height = letter_height, center = false)
translate([x3,y3,0])
rotate([0,0,ang])
{text(char,size = letter_size, font = font, halign = "center", valign = "center", $fn = 16);};
}