How to make a tetrahedron, and other platonic solids. How to make an octahedron, and other polyhedra from one balloon including the triangular dipyramid and cuboctahedron.

How to make an icosahedron, and other snub polyhedra including the snub cube. How to make a tangle of six squares, and other tangles: three rectangles, four triangles, and six pentagons

Make a few different tilings of the hyperbolic plane. How to make Sierpinski's Tetrahedron, a lovely fractal.

Gallery of Possibilities

	Five Intersecting Tetrahedra		A balloon-style octahedron, made out of one leg of a pair of tights stuffed with stuffing.
	A hyperboloid named Autumn.		Another view of Autumn.

The Mathematics Within

For more information about the mathematical theory behind these models, see Computational Balloon Twisting: The Theory of Balloon Polyhedra.