  We introduce the concept of a conical zeta value as a geometric
generalization of a multiple zeta value in the context of convex cones. The
quasi-shuffle and shuffle relations of multiple zeta values are generalized to
open cone subdivision and closed cone subdivision relations respectively for
conical zeta values. In order to achieve the closed cone subdivision relation,
we also interpret linear relations among fractions as subdivisions of decorated
closed cones. As a generalization of the double shuffle relation of multiple
zeta values, we give the double subdivision relation of conical zeta values and
formulate the extended double subdivision relation conjecture for conical zeta
values.
