  We investigate the folding problem that asks if a polygon P can be folded to
a polyhedron Q for given P and Q. Recently, an efficient algorithm for this
problem has been developed when Q is a box. We extend this idea to regular
polyhedra, also known as Platonic solids. The basic idea of our algorithms is
common, which is called stamping. However, the computational complexities of
them are different depending on their geometric properties. We developed four
algorithms for the problem as follows. (1) An algorithm for a regular
tetrahedron, which can be extended to a tetramonohedron. (2) An algorithm for a
regular hexahedron (or a cube), which is much efficient than the previously
known one. (3) An algorithm for a general deltahedron, which contains the cases
that Q is a regular octahedron or a regular icosahedron. (4) An algorithm for a
regular dodecahedron. Combining these algorithms, we can conclude that the
folding problem can be solved pseudo-polynomial time when Q is a regular
polyhedron and other related solid.
