Square pyramid

Square pyramid
Type	Pyramid, Johnson J92 – J1 – J2
Faces	4 triangles 1 square
Edges	8
Vertices	5
Vertex configuration	${\displaystyle 4\times (3^{2}\times 4)+1\times (3^{4})}$
Symmetry group	${\displaystyle C_{4\mathrm {v} }}$
Volume	${\displaystyle {\frac {1}{3}}l^{2}h}$
Dihedral angle (degrees)	Equilateral square pyramid: triangle-to-triangle: 109.47° square-to-triangle: 54.74°
Dual polyhedron	self-dual
Properties	convex, elementary (equilateral square pyramid)
Net

In geometry, a square pyramid is a pyramid with a square base and four triangles, having a total of five faces. If the apex of the pyramid is directly above the center of the square, it becomes a form of right pyramid with four isosceles triangles. When all of the pyramid's edges are equal in length, its triangles are all equilateral, an example of a Johnson solid.

Square pyramids have appeared throughout the history of architecture, with examples being Egyptian pyramids and many other similar buildings. They also occur in chemistry in square pyramidal molecular structures. Square pyramids are often used in the construction of other polyhedra and as the cell of a four-dimensional polytope called cubic pyramid. Square pyramidal number is a natural number that counts the number of spheres stacked into a square pyramid. Many mathematicians in ancient times discovered the formula for the volume of a square pyramid with different approaches.