  We address the question whether there is a three-dimensional bounded domain
such that the Neumann--Poincar\'e operator defined on its boundary has
infinitely many negative eigenvalues. It is proved in this paper that tori have
such a property. It is done by decomposing the Neumann--Poincar\'e operator on
tori into infinitely many self-adjoint compact operators on a Hilbert space
defined on the circle using the toroidal coordinate system and the Fourier
basis, and then by proving that the numerical range of infinitely many
operators in the decomposition has both positive and negative values.
