Infinity on High with a 54% decline during a post-Grammy week. The album rose to number three in its third week with 79,000 units sold. In its fourth week, the disc slipped to number four and sold 67,000 copies. "Infinity on High"s sales again fell in its fifth week, moving 58,000 copies and descending to number eight on the chart. In its sixth and last week in the top ten it fell to number nine and sold 43,000 copies. In April 2007, the album was certified Platinum by the Recording Industry Association of America (RIAA), denoting the shipment of one million copies. It
Duocylinder flat tops. This operation is equivalent to removing select vertices/pyramids from polytopes, but since the 3-sphere is smooth/regular you have to generalize the operation. The dihedral angle between the two 3-d hypersurfaces on either side of the ridge is 90 degrees. Parallel projections of the duocylinder into 3-dimensional space and its cross-sections with 3-dimensional space both form . Perspective projections of the duocylinder form torus-like shapes with the 'doughnut hole' filled in. The duocylinder is the limiting shape of duoprisms as the number of sides in the constituent polygonal prisms approach infinity. The duoprisms therefore serve as good polytopic approximations