Provided we made the frames thin enough, they wouldn't cut into each other anymore, and the result (shown to the right) would be an intricate woven nest of 5 tetrahedra. Suppose we replaced these pyramids with tetrahedral frames. Thus the left hand picture illustrates what five intersecting tetrahedra look like, and notice how all these pyramids are cutting into each other. Thus we could inscribe 5 distinct tetrahedra inside a dodecahedron! The result of doing this is shown below. This tetrahedron has 4 corners, and the dodecahedron has 20 corners total. If we were to take 4 equidistant corners of the dodecahedron and connect them with lines, the result would be a pyramid (a tetrahedron) inscribed in the dodecahedron. To the right is shown a dodecahedron - the classic polyhedra with 12 equal sides.

To construct an origami version it is essential to have a good understanding of the object's structure, which the accompanying pictures try to illustrate. Escher or like to thumb through geometry textbooks. Origami Geometric Constructions Five Intersecting Tetrahedra About the object This visually stunning object should be a familiar sight to those who frequent the landscapes of M.C.