The geometry of the shells define the Sydney Opera House. The shells were all taken from the same sphere. Each shell was made up of series of ribs formed by parallel lines. The shells intersect to create a look of sails. Engineers could not calculate the precise geometry for the shell until the forces and bending moments were known. These could not be calculated until the exact geometric form was established. Engineers work on computers for almost a year to develop the form of the shells. The Sydney Opera House was one of the first buildings in the world to use computers in its design process. 

Within the shells you can what appear to be acute angles and obtuse angles. Although formed from a sphere the shells seem to have the shape of an isosceles triangle. There are panels in the building made up of ceramic tiles. These tiles form tessellations that make repeated diamond patterns. The shells and the panels are supported by a huge rectangular base.