# Puzzles involving nets of polyhedra

Remarks on A Puzzling Cube by NRICH: It's necessary to see at least 5 of the faces to deduce all 6. The net used in this activity could be swapped out for a different net of a cube. We could also do this activity with other nets. In the case of a triangular prism, this activity becomes trivial, as all faces can be deduced from a single image. To make this activity harder, we could use a polyhedron with more faces. For example, to make the problem much more difficult, we could use a truncated icosahedron. It would also be nice to improve upon their interactive such that users can submit their answers and get an instant response as to whether their answer is right or wrong.

Remarks on Which Face? by NRICH: The first way in which this problem could be altered, is to choose a different symbol to be on top. For example, if the "tree" symbol is on top, then the bottom symbol changes. Another way we could alter the problem is to use a different net of a cube. And finally, yet another way to alter the problem is to use the net of a different solid.

Remarks on Presents by NRICH: This problem could be extended by considering the nexts of additional solids. It should be noted that for cylinders and cones, there are infinitely many nets. So it should be seen that every polyhedra has finitely many nets, while this is not necessarily the case for non-polyhedra.

Remarks on Cut Nets by NRICH: This problem could be altered by changing where the cuts are made, or changing the selection of solids. Another way to alter the problem is to cut each solid into 3 pieces instead of 2.