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A square pyramid has five vertices, eight edges, and five faces. One face, called the base of the pyramid, is a square; the four other faces are triangles. [2] Four of the edges make up the square by connecting its four vertices. The other four edges are known as the lateral edges of the pyramid; they meet at the fifth vertex, called the apex. [3]
The base regularity of a pyramid's base may be classified based on the type of polygon: one example is the star pyramid in which its base is the regular star polygon. [28] The truncated pyramid is a pyramid cut off by a plane; if the truncation plane is parallel to the base of a pyramid, it is called a frustum.
The volume of a tetrahedron can be obtained in many ways. It can be given by using the formula of the pyramid's volume: =. where is the base' area and is the height from the base to the apex. This applies for each of the four choices of the base, so the distances from the apices to the opposite faces are inversely proportional to the areas of ...
The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): = (+ +), where a and b are the base and top side lengths, and h is the height.
A square pyramid and the associated abstract polytope. Here, the elements of a square pyramid can be defined as the partially ordered set. One modern approach is based on the theory of abstract polyhedra. These can be defined as partially ordered sets whose elements are the vertices, edges, and faces of a polyhedron. A vertex or edge element is ...
A square pyramid of cannonballs at Rye Castle in England 4900 balls arranged as a square pyramid of side 24, and a square of side 70. The cannonball problem asks for the sizes of pyramids of cannonballs that can also be spread out to form a square array, or equivalently, which numbers are both square and square pyramidal. Besides 1, there is ...
The volume of a symmetric bipyramid is , where B is the area of the base and h the perpendicular distance from the base plane to either apex. In the case of a regular n - sided polygon with side length s and whose altitude is h , the volume of such a bipyramid is: n 6 h s 2 cot π n . {\displaystyle {\frac {n}{6}}hs^{2}\cot {\frac {\pi }{n}}.}
Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. [1] The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2]