Pyramids are interesting shapes than can be used for a variety of nonconventional home and garden projects. There are two main types of pyramids: the square pyramid and the tetrahedron. The angles on each pyramid, particularly the sides, are not 90 degrees and special considerations have to be made during design to ensure proper construction.
Types

Home pyramids come in a variety of sizes and are usually based on the square pyramid dimensions of the Great Pyramid of Giza, Egypt. A square pyramid has a square base and four triangle sides. Like the ancient Egyptians, some people believe that objects placed inside square pyramids receive special powers. Experiment for yourself.
Another distinctive pyramid is the tetrahedron all three sides and the base are identical triangles (equilateral). Tetrahedrons are fun because all sides are the same.
Geometry

The dimensions of the Pyramid of Giza are aesthetically pleasing. The slope of the four sides are each 51.8 degrees. The triangular sides come together at the top, known as the apex. The dihedral angleused to make miter joints in woodworkingis slightly over 76 degrees (http://www.earthmatrix.com/great/pyramid.htm).
A tetrahedral pyramid is made of four identical equilateral triangles (all sides the same length). The dihedral angle for a tetrahedron is about 70 degrees.
Solid, Stick and Sheet Pyramids

To make a solid pyramid out of wood or plastic, use a table or miter saw. To make a "golden" pyramid:
Step1: Set the saw blade angle at 51.8 degrees
Step 2: Pass each side of a square block through the blade.To make a stick square pyramid:
Step 1: Join four sticks to form the square base. The four edges of the sides can be the same length, but for a true Giza pyramid, the sides are slightly shorter than the base edges (22:23).
Step 2: Joint the side sticks to each corner.
Step 3: Raise the side sticks to the apex and join.Each side makes a triangle with an apex angle of 63.5 degrees and the two base angles should be 58.3 degrees.
To make a pyramid out of flat stock like board lumber, use the angles for the triangle sides from above. Miter the sides so the edges will fit together. The bottom or base side is cut at 51.8 degrees, and the edges where the triangles join must meet at the dihedral angle of 76 degrees; the sides that join the faces have to be cut at half that angle (38 degrees) to fit properly. For a tetrahedral pyramid, use a dihedral angle of 70 degrees for each of your identical triangles.