I'd call it a triangular building but the answer you are looking for is pyramid but that is NOT what a triangular building is called.
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square based is much stronger
A cable., The vertical triangular portion of the end of a building, from the level of the cornice or eaves to the ridge of the roof. Also, a similar end when not triangular in shape, as of a gambrel roof and the like., The end wall of a building, as distinguished from the front or rear side., A decorative member having the shape of a triangular gable, such as that above a Gothic arch in a doorway.
A cube has 6 faces and a triangular pyramid has 5 faces. So a cube has 1 more face than a triangular prism. But a triangular pyramid has four faces. You make the call. That is correct: A triangular prism has five faces, and a cube has six faces, but a triangular pyramid has four faces.
A triangular pyramid has 4 vertices, while a triangular prism has 6. Therefore, a triangular prism has 2 more vertices than a triangular pyramid.
Triangular Pyramid......... The faces are Triangular....