Standard UV map (equirectangular 2:1) to mercator (1:1)

gistfile1.txt

var geometry = new THREE.IcosahedronGeometry( 2, 5 );

for ( var i = 0, l = geometry.faceVertexUvs[ 0 ].length; i < l; i ++ ) {

	for ( var j = 0, jl = geometry.faceVertexUvs[ 0 ][ i ].length; j < jl; j ++ ) {

		var uv = geometry.faceVertexUvs[ 0 ][ i ][ j ];

		var a = uv.y * Math.PI - Math.PI / 2;
		a = Math.sin(a);
		uv.y = 0.5 - Math.log( ( 1 + a ) / ( 1 - a ) ) / ( 4 * Math.PI );
		uv.y = 1 - uv.y;
		
	}

}

geometry.uvsNeedUpdate = true;