Final answer:
The 'star' shape has a total of 24 faces. This total includes the 4 triangular faces from each of the 6 square-based pyramids added onto a cube, subtracting the original 6 faces of the cube because they become bases for the pyramids.
Step-by-step explanation:
The question pertains to a geometric construction involving a cube and square-based pyramids. The construction results in a three-dimensional 'star' shape with additional faces. To determine the number of faces on this star shape, we can calculate it as follows:
A cube has 6 faces. When a square-based pyramid is attached to each face of the cube, the base of each pyramid coincides with each face of the cube and thus does not add to the face count. However, each pyramid has 4 triangular faces. Since there are 6 pyramids, they add 24 triangular faces (6 pyramids times 4 faces each).
Adding the original faces of the cube with the additional faces of the pyramids, we have:
- 6 faces of the cube
- + 24 faces of the pyramids (6 pyramids × 4 faces each)
This gives us a total of 30 faces. However, each original face of the cube is now part of the base of a pyramid and is no longer visible as a separate face, so we must subtract the 6 original cube faces:
- 30 faces
- - 6 faces (subtracted because they are now pyramid bases)
Thus, the final total is 24 faces