Another pentahedron, the faces of this solid include a square, two equilateral triangles, and two trapezoids whose long edge is twice as long as the other three edges. It has the interesting property of being able to form a tetrahedron when joined to another of the same shape by the square face.

In an effort to complete a Periodic Table of Polyhedra in origami, I began to by producing the lower polyhedra. There are two unique pentahedra. One is a pyramid with a square base, and the other is the triangular prism. The one shown here is a "regular" triangular prism, having all edges of unit lengths and faces of regular polygons, and only a single type of vertex. I'm not sure why is it not considered an Archimedean solid; I guess because it bears no particular relationship to any Pythagorean solid.

Original method for folding the twenty-sided platonic solid from a single rectangular sheet of a 2:1 ratio. My method features good utilization of the paper and optimization for size, a easy and straightforward prefold sequence, and a very secure lock. In general, folding a polyhedron from a 2:1 rectangle is easier than a square and better utilizes the paper. This is because you have more edge relative to area, and you can use something like a Mercator projection for the layout, or a two-hemisphere clamshell arrangement.

This fourteen-sided Archimedean solid is one of my favorite shapes, and closely related to the Truncated Octahedron, but easier to fold. One of my first successful polyhedra designs.