Daniel's star
A solid 'star' shape is created. How many faces does it have?
Age
11 to 14
Challenge level
Problem
Daniel creates a solid 'star' shape by gluing square-based pyramids onto each face of a cube, so that the cube is completely hidden.
How many faces does his 'star' have?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
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 possible height of pyramid where the two faces that meet at each of the original edges become one face, giving a solid with 12 rhomboidal faces.