Abstract
Based on the art of curved crease origami, we give an example of the construction of a family of shapes from
mathematically ideal paper that consists of cylinders and cones and reassembles the structure of a spherical polyhedron
with regular faces. We offer explicit formulas to parametrize the crease curves. Moreover, we illustrate this method
on the five Platonic solids, which can be folded from one single sheet of paper.
