Second Stellation of the Cuboctahedron
This model is made using 7 different colors. Three of the colors are used to make faces that lie in the same planes as a cube. The other 4 colors are used to make faces that lie in the same planes as an octahedron. Parallel planes are made of the same colors. You will need to cut 48 right isosceles triangle pieces from 3 colors and 48 equilateral triangle pieces from 4 colors to complete this figure.
As you begin this model, you should notice that there are two interesting facial configurations.
(1) In the picture above and to the left, you can see a yellow, irregular octagram. Actually each side of that yellow octagram is created from 2 right isosceles triangles.
To give those side right isosceles triangle pieces more rigidity, Father Wenninger suggests cutting them out together with one long tab that connects them.
Two of those sections can be glued together while assembling your polyhedron to add even more rigidity. This detail is shown In the picture just above and to the right.
(2) The other interesting facial configuration is shown more clearly in this picture.
The blue pieces can be seen as a downward facing triangle with facets removed from each of its vertices.