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If the apex of the pyramid is directly above the center of the square, it is a right square pyramid with four isosceles triangles; otherwise, it is an oblique square pyramid. When all of the pyramid's edges are equal in length, its triangles are all equilateral. It is called an equilateral square pyramid, an example of a Johnson solid.
The surface area of a gyroelongated square bipyramid is 16 times the area of an equilateral triangle, that is: [4], and the volume of a gyroelongated square bipyramid is obtained by slicing it into two equilateral square pyramids and one square antiprism, and then adding their volume: [4] + +.
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The height of an elongated square pyramid can be calculated by adding the height of an equilateral square pyramid and a cube. The height of a cube is the same as the edge length of a cube's side, and the height of an equilateral square pyramid is ( 1 / 2 ) a {\displaystyle (1/{\sqrt {2}})a} .
Its dihedral angle can be obtained in a similar way as the elongated square pyramid, by adding the angle of square pyramids and a cube: [7] The dihedral angle of an elongated square bipyramid between two adjacent triangles is the dihedral angle of an equilateral triangle between its lateral faces, arccos ( − 1 / 3 ) ≈ 109.47 ∘ ...
Chinese pyramids. The John Hancock Center in Chicago, Illinois is a frustum whose bases are rectangles. The Washington Monument is a narrow square-based pyramidal frustum topped by a small pyramid. The viewing frustum in 3D computer graphics is a virtual photographic or video camera's usable field of view modeled as a pyramidal frustum.
A square bipyramid is a bipyramid constructed by attaching two square pyramids base-to-base. These pyramids cover their square bases, so the resulting polyhedron has eight triangular faces. [1] A square bipyramid is said to be right if the square pyramids are symmetrically regular and both of their apices are on the line passing through the ...
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.