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In this paper, we will describe the space spanned by the angle-sums of polytopes, recorded in the α-vector. We will consider the angles sums of simplices and the angles sums and face numbers of simplicial polytopes and general polytopes. We will construct families of polytopes whose angle sums span the spaces of poly-topes defined by the Gram and Perles… (More)

a r t i c l e i n f o a b s t r a c t For a given n × n matrix A, let k(A) stand for the maximal number of orthonormal vectors x j such that the scalar products Ax j , x j lie on the boundary of the numerical range W (A). This number was recently introduced by Gau and Wu and we therefore call it the Gau–Wu number of the matrix A. We compute k(A) for two… (More)

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