Can we extend Euler's formula to read: V-E+F-S=1, where S is the number of solids? If so, we may extend Euler's formula to any dimensional space to read: E0-E1+E2-E3+...=1, where Ek is the number of k-dimensional entities, with E0 representing the number of vertices, E1 the number of edges, E2 the number of faces, etc., insofar as the polytope is convex. The extended formula seems to be valid.

## Euler's Formula for Polyhedra

Can we extend Euler's formula to read: V-E+F-S=1, where S is the number of solids? If so, we may extend Euler's formula to any dimensional space to read: E0-E1+E2-E3+...=1, where Ek is the number of k-dimensional entities, with E0 representing the number of vertices, E1 the number of edges, E2 the number of faces, etc., insofar as the polytope is convex. The extended formula seems to be valid.