Two Intersecting Tetrahedra
(Stellated Octangula)
This figure is really a stellated octahedron. By using two colors to create the figure you can make your polyhedron look like two tetrahedra that pass through each other.
The template is below for making two intersecting tetrahedron. Each pattern makes one pyramidal point of one tetrahedron. You will need to cut out 8 of these shapes ... four pyramids of each of two colors ... and, as always, create tabs surrounding all outside edges.
Fold each shape along the fold lines and glue the two bottom edges to each other. You will now have a small bottomless pyramid.
To see the full sized template click on this image: 
On the three bottom edges of that pyramid attach 3 pyramid of the opposite color. In the above picture, 3 yellow pyramids are glued to the base of one blue pyramid. Continue this process by gluing 3 same colored pyramid to the base of every contrasting pyramid.
This polygon can also be built with 4 different colors and an equilateral triangle as the template. Assemble the bottomless pyramid from 3 different colors. Attach to the bottom of this pyramid 3 faces all of the same color.
To make this polyhedron in 4 different colors like the picture on the right above, use the template below.
To see the full sized template click on this image: 