#
# Constructs the five Platonic Solids.
#
#					Gershon Elber Dec. 1991.
#

g = (sqrt( 5 ) + 1) / 2; # The golden ratio
q = g - 1;

#
# Tetrahedron
#

v1 = vector(  1,  1,  1 );
v2 = vector(  1, -1, -1 );
v3 = vector( -1,  1, -1 );
v4 = vector( -1, -1,  1 );

pl1 = poly( list( v1, v3, v2 ), false );
pl2 = poly( list( v1, v4, v3 ), false );
pl3 = poly( list( v1, v2, v4 ), false );
pl4 = poly( list( v2, v3, v4 ), false );

tetra = mergepoly( list( pl1, pl2, pl3, pl4 ) );

interact( tetra );

save( "tetrahdr", tetra );

#
# Cube
#

v1 = vector( -1, -1, -1 );
v2 = vector( -1, -1,  1 );
v3 = vector( -1,  1,  1 );
v4 = vector( -1,  1, -1 );
v5 = vector(  1, -1, -1 );
v6 = vector(  1, -1,  1 );
v7 = vector(  1,  1,  1 );
v8 = vector(  1,  1, -1 );

pl1 = poly( list( v4, v3, v2, v1 ), false );
pl2 = poly( list( v5, v6, v7, v8 ), false );
pl3 = poly( list( v1, v2, v6, v5 ), false );
pl4 = poly( list( v2, v3, v7, v6 ), false );
pl5 = poly( list( v3, v4, v8, v7 ), false );
pl6 = poly( list( v4, v1, v5, v8 ), false );

cube = mergepoly( list( pl1, pl2, pl3, pl4, pl5, pl6 ) );

interact( cube );

#
# Octahedron
#

v1 = vector(  0,  0,  1 );
v2 = vector(  1,  0,  0 );
v3 = vector(  0,  1,  0 );
v4 = vector( -1,  0,  0 );
v5 = vector(  0, -1,  0 );
v6 = vector(  0,  0, -1 );

pl1 = poly( list( v1, v3, v2 ), false );
pl2 = poly( list( v1, v4, v3 ), false );
pl3 = poly( list( v1, v5, v4 ), false );
pl4 = poly( list( v1, v2, v5 ), false );
pl5 = poly( list( v6, v2, v3 ), false );
pl6 = poly( list( v6, v3, v4 ), false );
pl7 = poly( list( v6, v4, v5 ), false );
pl8 = poly( list( v6, v5, v2 ), false );

octa = mergepoly( list( pl1, pl2, pl3, pl4, pl5, pl6, pl7, pl8 ) );

interact( octa );

save( "octahdr", octa );

#
# Dodecahedron
#

v1  = vector(  0,  q,  g );
v2  = vector(  0, -q,  g );
v3  = vector(  1,  1,  1 );
v4  = vector(  1, -1,  1 );
v5  = vector( -1, -1,  1 );
v6  = vector( -1,  1,  1 );
v7  = vector( -g,  0,  q );
v8  = vector(  g,  0,  q );
v9  = vector(  q,  g,  0 );
v10 = vector( -q,  g,  0 );
v11 = vector( -q, -g,  0 );
v12 = vector(  q, -g,  0 );
v13 = vector( -g,  0, -q );
v14 = vector(  g,  0, -q );
v15 = vector(  1,  1, -1 );
v16 = vector( -1,  1, -1 );
v17 = vector( -1, -1, -1 );
v18 = vector(  1, -1, -1 );
v19 = vector(  0,  q, -g );
v20 = vector(  0, -q, -g );

pl1  = poly( list( v2, v1, v3, v8, v4 ), false );
pl2  = poly( list( v1, v2, v5, v7, v6 ), false );
#pl3  = poly( list( v1, v3, v9, v10, v6 ), false );
pl3  = poly( list( v6, v10, v9, v3, v1 ), false );
pl4  = poly( list( v2, v4, v12, v11, v5 ), false );
pl5  = poly( list( v4, v8, v14, v18, v12 ), false );
#pl6  = poly( list( v5, v7, v13, v17, v11 ), false );
pl6  = poly( list( v11, v17, v13, v7, v5 ), false );
pl7  = poly( list( v13, v16, v10, v6, v7 ), false );
pl8  = poly( list( v16, v19, v15, v9, v10 ), false );
pl9  = poly( list( v3, v9, v15, v14, v8 ), false );
pl10 = poly( list( v14, v15, v19, v20, v18 ), false );
pl11 = poly( list( v12, v18, v20, v17, v11 ), false );
#pl12 = poly( list( v17, v13, v16, v19, v20 ), false );
pl12 = poly( list( v20, v19, v16, v13, v17 ), false );

dodeca = mergepoly( list( pl1, pl2, pl3, pl4, pl5, pl6,
			  pl7, pl8, pl9, pl10, pl11, pl12 ) );

interact( dodeca );

save( "dodechdr", dodeca );

#
# Icosahedron (Note we construct only its upper half and reflect it).
#

v1  = vector(  1,  0,  g );
v2  = vector( -1,  0,  g );
v3  = vector(  0,  g,  1 );
v4  = vector(  0, -g,  1 );
v5  = vector(  g,  1,  0 );
v6  = vector( -g,  1,  0 );
v7  = vector( -g, -1,  0 );
v8  = vector(  g, -1,  0 );
v9  = vector(  0,  g, -1 );

pl1  = poly( list( v2, v3, v1 ), false );
pl2  = poly( list( v1, v4, v2 ), false );
pl3  = poly( list( v2, v6, v3 ), false );
pl4  = poly( list( v3, v5, v1 ), false );
pl5  = poly( list( v3, v9, v5 ), false );
pl6  = poly( list( v3, v6, v9 ), false );
pl7  = poly( list( v2, v7, v6 ), false );
pl8  = poly( list( v2, v4, v7 ), false );
pl9  = poly( list( v1, v8, v4 ), false );
pl10 = poly( list( v1, v5, v8 ), false );

icosa1 = mergepoly( list( pl1, pl2, pl3, pl4, pl5, pl6, pl7, pl8, pl9, pl10 ) );
icosa2 = icosa1 * rotx( 180 );
icosa = mergepoly( list( icosa1, icosa2 ) );
free( icosa1 );
free( icosa2 );

interact( icosa );

save( "icosahdr", icosa );

free( g );
free( q );

free( v1 );
free( v2 );
free( v3 );
free( v4 );
free( v5 );
free( v6 );
free( v7 );
free( v8 );
free( v9 );
free( v10 );
free( v11 );
free( v12 );
free( v13 );
free( v14 );
free( v15 );
free( v16 );
free( v17 );
free( v18 );
free( v19 );
free( v20 );

free( pl1 );
free( pl2 );
free( pl3 );
free( pl4 );
free( pl5 );
free( pl6 );
free( pl7 );
free( pl8 );
free( pl9 );
free( pl10 );
free( pl11 );
free( pl12 );

free( tetra );
free( cube );
free( octa );
free( dodeca );
free( icosa );