of Homogeneous Partitioning s of Space. 



87 



the pyramid and one pair of sides equal to one-third of the 

 basal edge of the pyramid ; the two pinakoid faces remain 



Fig. 3. 



squares, and the four prism faces become rhombs (fig. 4> 

 a & b). 



As stated explicitly under (1) a, the volume is supposed to 

 remain constant in all cases, this condition arising from the 

 original problem, in which two liquid phases were con- 

 sidered. As the calculation for the cube transformed into a 

 square prism is extremely simple, we will consider it before 

 describing the method adopted in the other cases. 



If a cube of unit edge and unit volume is transformed into 

 a square prism of the height L and the same volume, the 



