Sixth Stellation of the Icosahedron
This polyhedron is related to the third stellation of the icosahedron. The cups of the third stellation of the icosahedron are arranged in the same order but this stellation has sharp pentagonal pyramids in the center of each cup. This polyhedron requires 5 colors and contains 120 pieces to cut and assemble. If we can align the colors correctly, the finished polyhedron will show the arrangement pictured below. Pieces that are contained in the same plane will be the same color.
In the example photo above, you can see a pale green set of 6 pieces that are contained in the same plane. You can also see the plane that contains the dark purple pieces and the pale purple pieces.
To see the full-sized template click on this image:
Begin by creating a cup using the 5-sided template figure above and on the right. Make the cup from 5 of these pieces using the usual icosahedral color arrangement that is shown below.
(0) Y B O R G (3) R O Y G B
(1) B Y R O G (4) G R B Y O
(2) O B G R Y (5) Y G O B R
Assemble these dimples in a clockwise placement as seen looking into the dimple.
Then create a corresponding pentagonal pyramid using the same color arrangement as the previous cup. When you glue the pyramid into the cup your colors won't align perfectly. The pyramid will be rotated slightly counter clockwise to align to the cup properly.
Here's the tricky part. Number each of your dimples containing a pyramid according to the icosahedral arrangement number. Dimple # 0 will be surrounded by dimples 1, 2, 3, 4, and 5 in a clockwise pattern. Study the proper alignment to allow faces that are in the same plane to be in the same color. This planar pattern will look like the small white and green image above.
As has been usual in these stellated icosahedra, the color list above represents only one-half of the model. To create the other half of the model use the same 6 color arrangements listed above but assemble the dimples and sharp pyramids in reverse order = enantiomorphs. Label each dimple with the numbers 5-reverse, 4 reverse, etc.
Dimple #5 reverse will be directly across the polyhedron from dimple #5.