The regular 5-cell (or 4- simplex) is an example of a tetrahedral pyramid. The dual of a polyhedral pyramid is another polyhedral pyramid, with a dual base. The vertices and edges of polyhedral pyramids form examples of apex graphs, graphs formed by adding one vertex (the apex) to a planar graph (the graph of the base). The lateral facets are pyramid cells, each constructed by one face of the base polyhedron and the apex. In 4-dimensional geometry, a polyhedral pyramid is a 4-polytope constructed by a base polyhedron cell and an apex point. A n-dimensional simplex has the minimum n+1 vertices, with all pairs of vertices connected by edges, all triples of vertices defining faces, all quadruples of points defining tetrahedral cells, etc. The family of simplices represent pyramids in any dimension, increasing from triangle, tetrahedron, 5-cell, 5-simplex, etc. Higher-dimensional pyramids are constructed similarly.

For a solid pyramid, the centroid is 1/4 the distance from the base to the apex.Ī 2-dimensional pyramid is a triangle, formed by a base edge connected to a noncolinear point called an apex.Ī 4-dimensional pyramid is called a polyhedral pyramid, constructed by a polyhedron in a 3-space hyperplane of 4-space with another point off that hyperplane. The centroid of a pyramid is located on the line segment that connects the apex to the centroid of the base. It can be given an extended Schläfli symbol ( ) ∨, where h is the pyramid altitude and r is the inradius of the base. Right pyramids with a regular base Ī right pyramid with a regular base has isosceles triangle sides, with symmetry is C nv or, with order 2 n. Pyramids can be doubled into bipyramids by adding a second offset point on the other side of the base plane.Ī pyramid cut off by a plane is called a truncated pyramid if the truncation plane is parallel to the pyramid's base, it is called a frustum. In a tetrahedron these qualifiers change based on which face is considered the base.

A right-angled pyramid has its apex above an edge or vertex of the base. A triangle-based pyramid is more often called a tetrahedron.Īmong oblique pyramids, like acute and obtuse triangles, a pyramid can be called acute if its apex is above the interior of the base and obtuse if its apex is above the exterior of the base. When unspecified, a pyramid is usually assumed to be a regular square pyramid, like the physical pyramid structures. A regular pyramid has a regular polygon base and is usually implied to be a right pyramid. Nonright pyramids are called oblique pyramids. All pyramids are self-dual.Ī right pyramid has its apex directly above the centroid of its base. A pyramid with an n-sided base has n + 1 vertices, n + 1 faces, and 2 n edges. Each base edge and apex form a triangle, called a lateral face. In geometry, a pyramid (from Ancient Greek πυραμίς ( puramís)) is a polyhedron formed by connecting a polygonal base and a point, called the apex. The 1- skeleton of pyramid is a wheel graph

Triangular pyramid net