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Daniel's Star

Stage: 3 and 4 Short Challenge Level: Challenge Level:1
Each pyramid has five faces, but the square base is glued onto the cube, and so is not a face of the star. There are 6 pyramids, each contributing 4 faces, so the star has 24 faces.

There is one height of pyramid which will make the two faces that meet at each of the original edges become one face, giving a solid with 12 rhomboidal faces.

This problem is taken from the UKMT Mathematical Challenges.
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