The dipyramids are the dual polyhedra of the uniform prisms, which are right prisms with regular polygonal bases and equal edge lengths (Figure 3a). This operation hides the original "base" that gives the dipyramid its name. Some examples are the pentagrammic and the heptagrammic pyramids shown in Figure 3.įigure 2: Some star pyramids (click on the image to get a 3D view that you can zoom and rotate).Ī closely related polyhedron is the dipyramid (or bipyramid), which is formed by joining two pyramids base to base (Figure 3b). Pyramids with a regular star polygon as its base are known as star pyramids. These last two pyramids approximate very well the Squaring of the Circle. However, there are some special square pyramids, such as the Golden pyramid, in which the b:h:a triangle in Figure 1 is a Kepler triangle (its sides obey the progression 1 : φ : φ ), or the square pyramid whose height to base ratio equals h:b=4:π like the Great Pyramid of Giza. In general, given a regular polygonal face, the pyramid's height can take any value. There are only three pyramids whose bases are a regular polygon ang whose edges are all equal: the tetrahedron, the square pyramid and the pentagonal pyramid (Figure 2).įigure 2: Pyramids with regular polygonal base and equal edges (click on the image to get a 3D view that you can zoom and rotate). The segment that connects the apex to the midpoint of a base edge is called the apotem (Figure 1).įigure 1: A general square pyramid of base 2b, height h and apotem a. If the base is a regular polygon and the apex is perpendicularly above the center of the polygon, the pyramid is symmetric. When unspecified, the base is usually assumed to be square. A pyramid is a polyhedron formed by connecting each vertex of a polygonal base to a point called the apex.
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