Infinity on High finished the year at number twenty-one on IFPI's list of the "Top 50 Global Best Selling Albums of 2007". "Infinity on High" has shipped over two million copies worldwide. The album also charted inside the top five worldwide, making it the band's most successful and breakthrough album internationally. "Infinity on High" charted all over Europe, debuting at number eight on "Billboard"'s European Albums chart. In Australia, it debuted at its peak of number four on the Australian ARIA Albums Chart. It remained on the Australian chart for a total of fifty weeks, spending its first seven weeks in the top
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