Why do this problem?
is very good to have pupils explore some special properties of solid shapes. It is particularly good in that the solutions do not appear very obviously.
Introduce the pupils gradually to the recognition of what are vertices and what are edges. Most pupils will then be needing to handle the shapes unless they are gifted in visualisation.
Tell me about your shape.
What vertices have you used?
Extensions are included in the last part of the activity.
Shapes made from pipe-cleaners and straws can be a useful aid