A triangular pyramid is a simple polyhedron. It has four faces, four vertices, six sides, four trihedral angles, six dihedral angles and twelve face angles. If the four vertices are A, B, C and D respectively, it can be recorded as tetrahedron ABCD, and when it is regarded as a triangular pyramid with vertices, it can also be recorded as a triangular pyramid A-BCD.

Each vertex of a tetrahedron has a unique face that does not pass through it, which is called the opposite of the vertex. The original vertex is called the opposite of this face. Of the six sides of a tetrahedron, two that have no common endpoint are called opposite sides. A tetrahedron has three opposite sides, and the line segments (three lines) connecting the midpoints of the sides are equally divided at the same point, that is, the center of gravity of the tetrahedron, also called the center of mass of the tetrahedron.

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The origin of triangular pyramid:

In the mathematical papyrus of Rhind BC 1650, pyramids have been studied by geometricians as mathematical objects. Questions 56 to 59 in papyrus are about the calculation of the relationship between the bottom, height and dihedral angle formed by the bottom and side of a square cone. If the height and length of the bottom are known, find the dihedral angle.

Legend has it that in the Elements of Geometry written by Euclid in the third century BC, the seventh proposition in chapter 12 proved that the volume of a triangular prism is three times that of a triangular pyramid with the same base and height, but there is no direct pyramid volume formula in the Elements of Geometry.

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