pyramids and prisms and Euler

these are representations of the pyramid family:

what do they all have in common?

how would you describe a pyramid to someone who wasn't clear (or over the phone)?













why are there the same number of faces as there are vertices for any pyramid?

what is the relationship between the number of arcs and the number of vertices for any pyramid?
why?

Euler's relationship is F + V = E + 2
faces + vertices = edges + 2

why must this be true for any pyramid?


these are representations of some of the prism family:

what is a common feature of this family of solids?

















can you explain why for every prism, the numbers of vertices and the numbers of edges are in the same multiplication table?

what is the relationship between the number of faces and the number of vertices for any prism?
why?

why must Euler's relationship (F + V = E + 2)
be true for any prism?