Square pyramid

In geometry, a square pyramid is a pyramid with a square base, having a total of five faces. 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, and it is called an equilateral square pyramid.

Square pyramid
Type	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	${\displaystyle C_{4v}}$
Volume	${\displaystyle {\frac {1}{3}}l^{2}h}$
Dual polyhedron	self-dual
Properties	convex
Net

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. Many mathematicians in ancient times discovered the formula for the volume of a square pyramid with different approaches.