Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 447462 (2006) 

Vector spaces spanned by the angle sums of polytopesKristin A. CamengaCornell University, Ithaca, NY, email: kacam@math.cornell.eduAbstract: This paper describe the spaces spanned by the angle sums of certain classes of polytopes, as recorded in the $\alpha_{}$vector. Families of polytopes are constructed whose angle sums span the spaces of polytopes defined by the Gram and Perles equations, analogs of the Euler and DehnSommerville equations. This shows that the dimension of the affine span of the space of angle sums of simplices is $\left\lfloor \frac{d1}{2}\right\rfloor$, and that of the combined angle sums and face numbers of simplicial polytopes and general polytopes are $d1$ and $2d3$, respectively. A tool used in proving these results is the $\gamma$vector, an angle analog to the $h$vector. Full text of the article:
Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.
© 2007 Heldermann Verlag
