  We demonstrate that the original fundamental allometry alone cannot
accurately describe the relationship between urban area and population size.
Instead, building height is a third factor that interplays with area and
population. To illustrate this, we propose a straightforward model based on the
idea that city area is the result of people's desire to live close to one
another while also having sufficient living space. This leads to a more general
form of fundamental allometry (relating area, population, and building height).
Our argument is supported by empirical data from different countries.
