% Based on coordinate lists for polyhedra at http://www.rwgrayprojects.com/Lynn/Coordinates/coord01.html

pts = zeros(62,3);
pts(1,:)=	[0	0	2*1.6180339887^2];
pts(2,:)=	[1.6180339887^2	0	1.6180339887^3];
pts(3,:)=	[1.6180339887	1.6180339887^2	1.6180339887^3];
pts(4,:)=	[0	1.6180339887	1.6180339887^3];
pts(5,:)=	[-1.6180339887	1.6180339887^2	1.6180339887^3];
pts(6,:)=	[-1.6180339887^2	0	1.6180339887^3];
pts(7,:)=	[-1.6180339887	-1.6180339887^2	1.6180339887^3];
pts(8,:)=	[0	-1.6180339887	1.6180339887^3];
pts(9,:)=	[1.6180339887	-1.6180339887^2	1.6180339887^3];
pts(10,:)=	[1.6180339887^3	1.6180339887	1.6180339887^2];
pts(11,:)=	[1.6180339887^2	1.6180339887^2	1.6180339887^2];
pts(12,:)=	[0	1.6180339887^3	1.6180339887^2];
pts(13,:)=	[-1.6180339887^2	1.6180339887^2	1.6180339887^2];
pts(14,:)=	[-1.6180339887^3	1.6180339887	1.6180339887^2];
pts(15,:)=	[-1.6180339887^3	-1.6180339887	1.6180339887^2];
pts(16,:)=	[-1.6180339887^2	-1.6180339887^2	1.6180339887^2];
pts(17,:)=	[0	-1.6180339887^3	1.6180339887^2];
pts(18,:)=	[1.6180339887^2	-1.6180339887^2	1.6180339887^2];
pts(19,:)=	[1.6180339887^3	-1.6180339887	1.6180339887^2];
pts(20,:)=	[1.6180339887^3	0	1.6180339887];
pts(21,:)=	[1.6180339887^2	1.6180339887^3	1.6180339887];
pts(22,:)=	[-1.6180339887^2	1.6180339887^3	1.6180339887];
pts(23,:)=	[-1.6180339887^3	0	1.6180339887];
pts(24,:)=	[-1.6180339887^2	-1.6180339887^3	1.6180339887];
pts(25,:)=	[1.6180339887^2	-1.6180339887^3	1.6180339887];
pts(26,:)=	[2*1.6180339887^2	0	0];
pts(27,:)=	[1.6180339887^3	1.6180339887^2	0];
pts(28,:)=	[1.6180339887	1.6180339887^3	0];
pts(29,:)=	[0	2*1.6180339887^2	0];
pts(30,:)=	[-1.6180339887	1.6180339887^3	0];
pts(31,:)=	[-1.6180339887^3	1.6180339887^2	0];
pts(32,:)=	[-2*1.6180339887^2	0	0];
pts(33,:)=	[-1.6180339887^3	-1.6180339887^2	0];
pts(34,:)=	[-1.6180339887	-1.6180339887^3	0];
pts(35,:)=	[0	-2*1.6180339887^2	0];
pts(36,:)=	[1.6180339887	-1.6180339887^3	0];
pts(37,:)=	[1.6180339887^3	-1.6180339887^2	0];
pts(38,:)=	[1.6180339887^3	0	-1.6180339887];
pts(39,:)=	[1.6180339887^2	1.6180339887^3	-1.6180339887];
pts(40,:)=	[-1.6180339887^2	1.6180339887^3	-1.6180339887];
pts(41,:)=	[-1.6180339887^3	0	-1.6180339887];
pts(42,:)=	[-1.6180339887^2	-1.6180339887^3	-1.6180339887];
pts(43,:)=	[1.6180339887^2	-1.6180339887^3	-1.6180339887];
pts(44,:)=	[1.6180339887^3	1.6180339887	-1.6180339887^2];
pts(45,:)=	[1.6180339887^2	1.6180339887^2	-1.6180339887^2];
pts(46,:)=	[0	1.6180339887^3	-1.6180339887^2];
pts(47,:)=	[-1.6180339887^2	1.6180339887^2	-1.6180339887^2];
pts(48,:)=	[-1.6180339887^3	1.6180339887	-1.6180339887^2];
pts(49,:)=	[-1.6180339887^3	-1.6180339887	-1.6180339887^2];
pts(50,:)=	[-1.6180339887^2	-1.6180339887^2	-1.6180339887^2];
pts(51,:)=	[0	-1.6180339887^3	-1.6180339887^2];
pts(52,:)=	[1.6180339887^2	-1.6180339887^2	-1.6180339887^2];
pts(53,:)=	[1.6180339887^3	-1.6180339887	-1.6180339887^2];
pts(54,:)=	[1.6180339887^2	0	-1.6180339887^3];
pts(55,:)=	[1.6180339887	1.6180339887^2	-1.6180339887^3];
pts(56,:)=	[0	1.6180339887	-1.6180339887^3];
pts(57,:)=	[-1.6180339887	1.6180339887^2	-1.6180339887^3];
pts(58,:)=	[-1.6180339887^2	0	-1.6180339887^3];
pts(59,:)=	[-1.6180339887	-1.6180339887^2	-1.6180339887^3];
pts(60,:)=	[0	-1.6180339887	-1.6180339887^3];
pts(61,:)=	[1.6180339887	-1.6180339887^2	-1.6180339887^3];
pts(62,:)=	[0	0	-2*1.6180339887^2];

% Octahedron faces
faces = zeros(8,3);
faces(1,:) = [7, 10, 43];
faces(2,:) = [7, 22, 10];
faces(3,:) = [7, 43, 49];
faces(4,:) = [7, 49, 22];
faces(5,:) = [55, 10, 43];
faces(6,:) = [55, 22, 10];
faces(7,:) = [55, 43, 49];
faces(8,:) = [55, 49, 22];

% As triangles:
X = zeros(3,8);
Y = zeros(3,8);
Z = zeros(3,8);
C = [0.5000 1.0000 1.0000 0.5000 0.5000 1.0000 1.0000 0.5000;
     1.0000 0.5000 0.5000 0.1667 1.0000 0.5000 0.5000 0.1667;
     0.3330 0.3330 0.5000 0.5000 0.3330 0.3330 0.5000 0.5000];
% this part is still muddy
for i = 1:8
    pt = zeros(3,3);
    pt(1,:) = pts(faces(i,1),:);
    pt(2,:) = pts(faces(i,2),:);
    pt(3,:) = pts(faces(i,3),:);
    for j = 1:3
        X(j,i) = pt(j,1);
        Y(j,i) = pt(j,2);
        Z(j,i) = pt(j,3);
    end
end
figure;
fill3(X,Y,Z,C);

% Dodecahedron faces
faces = zeros(36,3);
 faces( 1,:) = [ 4, 8, 11];
 faces( 2,:) = [11, 8, 18];
 faces( 3,:) = [11, 18, 20];
 faces( 4,:) = [ 4, 13, 23];
 faces( 5,:) = [ 4, 23, 8];
 faces( 6,:) = [ 8, 23, 16];
 faces( 7,:) = [ 4, 11, 28];
 faces( 8,:) = [ 4, 28, 30];
 faces( 9,:) = [ 4, 30, 13];
 faces(10,:) = [ 8, 16, 34];
 faces(11,:) = [ 8, 34, 18];
 faces(12,:) = [18, 34, 36];
 faces(13,:) = [11, 20, 28];
 faces(14,:) = [20, 45, 28];
 faces(15,:) = [20, 38, 45];
 faces(16,:) = [13, 30, 23];
 faces(17,:) = [23, 30, 41];
 faces(18,:) = [41, 30, 47];
 faces(19,:) = [16, 23, 34];
 faces(20,:) = [34, 23, 50];
 faces(21,:) = [50, 23, 41];
 faces(22,:) = [18, 36, 52];
 faces(23,:) = [18, 52, 38];
 faces(24,:) = [18, 38, 20];
 faces(25,:) = [28, 45, 56];
 faces(26,:) = [28, 56, 47];
 faces(27,:) = [28, 47, 30];
 faces(28,:) = [34, 50, 60];
 faces(29,:) = [34, 60, 36];
 faces(30,:) = [36, 60, 52];
 faces(31,:) = [38, 52, 60];
 faces(32,:) = [38, 60, 56];
 faces(33,:) = [38, 56, 45];
 faces(34,:) = [41, 47, 56];
 faces(35,:) = [41, 56, 60];
 faces(36,:) = [41, 60, 50];

% As triangles:
X = zeros(3,36);
Y = zeros(3,36);
Z = zeros(3,36);
% this part is still muddy
for i = 1:36
    pt = zeros(3,3);
    pt(1,:) = pts(faces(i,1),:);
    pt(2,:) = pts(faces(i,2),:);
    pt(3,:) = pts(faces(i,3),:);
    for j = 1:3
        X(j,i) = pt(j,1);
        Y(j,i) = pt(j,2);
        Z(j,i) = pt(j,3);
    end
end
figure;
fill3(X,Y,Z,'c');