One side of a square would be untouched with only 3 triangle faces attached to it. To make an entire closed shape, it would need another part or some 3 dimensional bending would need to take place. A pyramid has 1 square face and 4 triangle faces. A pyramid could also have 4 triangle faces where one triangle substitutes the square face.
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The only one i can think of is the square - based pyramid, with 4 triangular faces and 1 square
They can be any shape ! We have square and rectangular ones in my town (and there's at least a couple of triangular ones too !)
A triangular pyramid is a four sided 3D shape. All four sides are triangles. It resembles a 'traditional' pyramid, like the ones in Egypt. A triangular prism is a five sided 3D shape. It consists of two identical triangular sides connected by three identical rectangular sides. think of it as a cylinder with triangles on the ends and three sides instead of a smooth surface.
In math terms, a pyramid could have a square base, triangular base or another shape. The Egyptian pyramids (and Aztec ones) had a square base. So they had 8 edges (for on the base and 4 rising to the top) and 5 faces (4 facing up and the base).
Most of the common ones have already been named, so I will not be naming any. Prisms and pyramids are named according to the 2-dimensional shape of their base(s). For example, triangular prism or square based pyramid.