Four Platonic Solids by John Montroll
Number of units: One sheet per solid
Designer: John Montroll
In the book A Plethora of Polyhedra in Origami (120 pages, 2002) by John Montroll.
Comments: Each solid is made from a single sheet of paper, unlike modular origami models which are made from multiple sheets of paper. Instructions for solids start becoming complex as the number of vertices and edges increases.