Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

Each base edge and apex form a triangle, called a lateral face.

The word "pyramid" derives from the ancient Greek term "πυραμίς" (pyramis), which referred to a pyramid-shaped structure and a type of wheat cake.

[1][2] The term is rooted in the Greek "πυρ" (pyr, 'fire') and "άμις" (amis, 'vessel'), highlighting the shape's pointed, flame-like appearance.

[3] In Byzantine Greek, the term evolved to "πυραμίδα" (pyramída), continuing to denote pyramid structures.

[5][6] A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the apex.

Each base edge and apex form an isosceles triangle called a lateral face.

Euclides in his Elements defined a pyramid as a solid figure, constructed from one plane to one point.

The context of his definition was vague until Heron of Alexandria defined it as the figure by putting the point together with a polygonal base.

[9] A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces as triangles, trapezoids, and parallelograms.

Other sources define only the term right pyramid to include within its definition the regular base[16].

[21][22] A tetrahedron or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base.

[25] Pyramids have the property of self-dual, meaning their duals are the same as vertices corresponding to the edges and vice versa.

The pyramid height is defined as the length of the line segment between the apex and its orthogonal projection on the base.