Triangular Pyramid......... The faces are Triangular....
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a pyramid does.
The solid shape that has one square face and four triangular faces is called a pyramid. If you were to have a shape that had four triangular faces and no square face, it would be called a triangular pyramid.
The 3D shape you are describing is a pentagonal pyramid. It has a pentagonal base with five sides, and five vertices where the triangular faces meet. The three rectangle faces are lateral faces that connect the triangular base to the apex of the pyramid. The pentagonal pyramid is a type of pyramid with a polygonal base and triangular faces.
A triangular based pyramid (tetrahedron) has 4 triangular faces, 6 edges and 4 vertices.
Pyramid, but to be exact it would be a Triangular Pyramid ;) * * * * * To be exact ... but WRONG! A triangular pyramid has 4 faces and 4 vertices! A shape with 5 faces and vertices is a quadrilateral based pyramid - of which a special case would be a square based pyramid.