at the bottom is is a square and triangle on the sides
a square pyramid
A square pyramid is a pyramid whose base is in the shape of a square.
It could be a square based pyramid
A square based pyramid perhaps.
a square based pyramid is a square at the bottom and a pyramid at the top
square based pyramid,
A square!
The difference is the shape. A cube is a 3D square. A square pyramid is a pyramid with for sides and a square on the bottom.
Unlike a tetrahedron (a four-faced shape with all triangular faces), a pyramid has a square (or rhomboid) base and triangular sides. Thus, a view from any side will yield a triangular appearance, while a view from below or above shows a square or rectangular shape.
It looks the same as a normal pyramid, the only difference is the base of the pyramid is square.
A Pyramid
A square based pyramid.