  In 1973, J. Cheeger and J. Simons raised the following question that still
remains open and is known as the Rational Simplex Problem: Given a geodesic
simplex in the spherical 3-space so that all of its interior dihedral angles
are rational multiples of $\pi$, is it true that its volume is a rational
multiple of the volume of the 3-sphere? We propose an analytical approach to
the Rational Simplex Problem by deriving a function $f(t)$, defined as an
integral of an elementary function, such that if there is a rational $t$, close
enough to zero, such that the value $f(t)$ is an irrational number then the
answer to the Rational Simplex Problem is negative.
