  This paper addresses the computation of normalized solid angle measure of
polyhedral cones. This is well understood in dimensions two and three. For
higher dimensions, assuming that a positive-definite criterion is met, the
measure can be computed via a multivariable hypergeometric series. We present
two decompositions of full-dimensional simplicial cones into finite families of
cones satisfying the positive-definite criterion, enabling the use of the
hypergeometric series to compute the solid angle measure of any polyhedral
cone. Additionally, our second decomposition method yields cones with a special
tridiagonal structure, reducing the number of required coordinates for the
hypergeometric series formula. Furthermore, we investigate the convergence of
the hypergeometric series for this case. Our findings provide a powerful tool
for computing solid angle measures in high-dimensional spaces.
