The Phoenix  is a minimalist approach to brewing coffee based on fundamentals of geometry, physics and chemistry.  It is a  framework to support a paper filter.  The paper filter and the Phoenix together create the geometry of the brew column.  The geometry of the brew column is a key element in the coffee brewing process.  By changing the shape of the brew column you will alter the characteristics of the coffee that is brewed through it.
 
Depending on the type of the coffee being brewed, volume of desired output, and targeted cup profile there is a corresponding  brew column shape that will optimize your success in brewing.