Alastair and Adam nets

Triangle based pyramid has four faces, four vertices. (#f = #v)
Square based pyramid has five faces, five vertices. (#v = #sides on base + 1)
Pentagonal pyramid has six faces, six vertices.(#f = # sides on base + 1)
Hexagonal pyramid has seven faces, seven vertices. (#f = #bases + #of vertices on base)
Triangular prism has five faces, six vertices. (#v = #f + 1, additional increment of one when going up in base sides)
Cube has six faces, eight vertices. (#sides on base *2 = #v)
Pentagonal prism has seven faces, ten vertices. (#v = # vertices on base *2)
Hexagonal prism has eight faces, twelve vertices. (#f = #sides of base + 2)