  Given a conformal data on a flat Euclidean space, we use crosscap conformal
bootstrap equations to numerically solve the Lee-Yang model as well as the
critical Ising model on a three-dimensional real projective space. We check the
rapid convergence of our bootstrap program in two-dimensions from the exact
solutions available. Based on the comparison, we estimate that our systematic
error on the numerically solved one-point functions of the critical Ising model
on a three-dimensional real projective space is less than one percent. Our
method opens up a novel way to solve conformal field theories on non-trivial
geometries.
