function [pos, tri] = icosahedron()

% ICOSAHEDRON creates an icosahedron
%
% [pos, tri] = icosahedron
% creates an icosahedron with 12 vertices and 20 triangles
% 
% See also OCTAHEDRON, ICOSAHEDRON42, ICOSAHEDRON162, ICOSAHEDRON642, ICOSAHEDRON2562

% Copyright (C) 2002, Robert Oostenveld
%
% This file is part of FieldTrip, see http://www.ru.nl/neuroimaging/fieldtrip
% for the documentation and details.
%
%    FieldTrip is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 3 of the License, or
%    (at your option) any later version.
%
%    FieldTrip is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%
%    You should have received a copy of the GNU General Public License
%    along with FieldTrip. If not, see <http://www.gnu.org/licenses/>.
%
% $Id: icosahedron.m 10772 2015-10-14 07:36:57Z roboos $

tri = [
   1   2   3
   1   3   4
   1   4   5
   1   5   6
   1   6   2
   2   8   3
   3   9   4
   4  10   5
   5  11   6
   6   7   2
   7   8   2  
   8   9   3  
   9  10   4  
  10  11   5  
  11   7   6  
  12   8   7
  12   9   8
  12  10   9
  12  11  10
  12   7  11
];

pos = zeros(12, 3);

rho=0.4*sqrt(5);
phi=2*pi*(0:4)/5;

pos( 1, :) = [0 0  1];          % top point

pos(2:6, 1) = rho*cos(phi)';
pos(2:6, 2) = rho*sin(phi)';
pos(2:6, 3) = rho/2;

pos(7:11, 1) = rho*cos(phi - pi/5)';
pos(7:11, 2) = rho*sin(phi - pi/5)';
pos(7:11, 3) = -rho/2;

pos(12, :) = [0 0 -1];          % bottom point

