No.
Whereas a tetrahedron has four triangular faces, at any point in time only one of them may be called a base.
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if its a four sided pyramid then four. if its a three sided pyramid then four.
The number of bases they do not have in common. A pyramid has one base, but a prism has two bases.
The only pyramid with exactly four faces is the triangular pyramid.
A triangular pyramid, also known as a tetrahedron, has four faces. This three-dimensional geometric shape is made up of four triangular bases.
A four sided pyramid is called a square based pyramid. It has a square base and four sides,(called edges,) that join at the apex. (the top of the pyramid.)