This graph denes the three dierent scales for spherical buildings. The ideal cube and sphere are plotted as in the previous denition graphs but here the surface area to volume ratio is plotted relative to the rough diameter of the building. When the diameter of a building is small the surface area to volume ratio increases and when the diameter is large the surface area to volume ratio decreases. This can be understood by inspecting the equations for the volume and surface area of a sphere. Because of this change in surface area to volume ratio based on building scale a program to scale correspondence exists. The two scale thresholds are indicated by vertical dotted lines.

The graph above establishes the definition of the spherical building type. The red line shows the surface area to volume ratio of a perfect geometric sphere. The black line shows the surface area to volume ratio of a perfect cube. The dotted black line shows the empirically determined variability in the type while still being close enough to the ideals to be considered spherical. The gray shaded region is the area of the graph that is considered spherical. No geometric shape can have a smaller surface area to volume ratio than a perfect sphere so the gray region never goes above the red line. Deviations from the ideals beyond a certain threshold cannot still be considered spherical and therefore the dotted line bounds the bottom of the gray region.

Buildings are plotted as points indicating their surface area to volume ratio. Buildings that fall within the gray region are considered spherical and shown as black dots. Buildings of the tower type are shown as red dots, at horizontal buildings are shown in green, and at vertical buildings are shown in blue. The zoomed out graph on the left shows that spherical buildings don’t get as large as at horizontal or at vertical buildings. Also the largest buildings on the graph, the Mall of America and Mies’ Chicago Convention center have relatively large surface areas for their enclosed volumes.