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A pyramid shape, by default, has a square base. It therefore has 5 faces.
Its shape, the number of faces edges and vertices.
A triangular based pyramid has 4 faces and 4 vertices
The number of faces determines the bases' shape.
A pyramid has a variable number of triangular faces. The base of a triangle can be practically any regular shape, starting with a triangle. Technically a pyramid can have four or more triangles as faces.