Yes, any one of their faces could be considered a base.
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Prisms, regular polyhedra.
dodecahedron
There are only 5 regular polyhedra: those with 4, 6, 8, 12 and 20 faces. If you know of 7 polyhedra there may be a Fields Medal (the Nobel prize for mathematicians) for you!
They are regular polyhedra.
dodecahedron