The report introduces the notion of isoperimetric quotient of a polyhedron. The isoperimetric quotient represents how spherical is a given polyhedron. A polyhedral graph can be drawn in the three-dimensional space. As the coordinates of vertices belonging to the same face may not be coplanar, the usual definition of isoperimetric quotient fails. A method based on a proper triangulation is developed, which enables extending the definition of isoperimetric quotient and compute it for any three-dimensional drawing. The isoperimetric quotients of C_12(I_h) and a number of isolated-pentagon fullerenes, with up to 82 vertices, are calculated. All fullerenes have high isoperimetric quotient and are spheroidal and all faces are periplanar. The discontinuity for smaller fullerenes is greater than the one for larger fullerenes, which makes problematic to choose C_60 as a benchmark. Provisional conclusions follow. (1). A polyhedral graph can be drawn in a variety of ways in three-dimensional space. As the coordinates of vertices belonging to the same face may not be coplanar, the usual definition of isoperimetric quotient fails. A method based on a proper triangulation is developed, which enables extending the definition of isoperimetric
quotient and compute it for any three-dimensional drawing. (2)The numbers of vertices, edges and faces show great degeneracies especially for numerous vertices. The result, together with some collinearities (Euler's formula), could limit the extensive applicability of these geometric parameters. (3) The isoperimetric quotient results for C_12(I_h), and isolated pentagon fullerenes with up to 82 vertices, are calculated. All fullerenes have high isoperimetric quotient and are spheroidal and all faces are periplanar. (4) A discussion of fullerene aromatic character is problematic because of the difficulty in choosing a benchmark. (5) The striking similarity between Euler's equation for simple polyhedra and Gibbs' phase rule was discussed by several authors: arguments were advanced for and against the analogy.