This paper presents the principles of foldable 3-D polyhedron air-coupled origami inductors and their application in multiphase interleaved MHz power conversion. The polyhedron air-coupled origami inductor comprises of multiple windings forming the surfaces of a closed Euclidean structure, with each of these surfaces representing one phase of the coupled inductor. These windings can be implemented on a printed circuit board (PCB) which can be folded to form the 3-D polyhedron strcutures. Compared to discrete air-core inductors, the polyhedron air-coupled inductor offers reduced volume of flux distribution, reduced current ripple, as well as a faster transient response. A four-phase interleaved boost converter with a symmetric tetrahedron air-coupled inductor as the input inductor was built and tested at switching frequencies from 1 MHz to 10 MHz to verify the principles of the polyhedron air-coupled inductors.