  We prove, in the case of hyperbolic 3-space, a couple of conjectures raised
by J. J. Seidel in "On the volume of a hyperbolic simplex", Stud. Sci. Math.
Hung. 21, 243-249, 1986. These conjectures concern expressing the volume of an
ideal hyperbolic tetrahedron as a monotonic function of algebraic maps. More
precisely, Seidel's first conjecture states that the volume of an ideal
tetrahedron in hyperbolic 3-space is determined by (the permanent and the
determinant of) the doubly stochastic Gram matrix $G$ of its vertices; Seidel's
fourth conjecture claims that the mentioned volume is a monotonic function of
both the permanent and the determinant of $G$.
