Polyhedral pyramid
Encyclopedia
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a polyhedral pyramid is a 4-polytope constructed by a base polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
cell and an apex
Apex (geometry)
In geometry, an apex is the vertex which is in some sense the highest of the figure to which it belongs.*In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side....
point. The lateral facets are pyramid
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. It is a conic solid with polygonal base....
cells, each constructed by one face of the base polyhedron and the apex.
A 4-simplex is an example of a tetrahedral pyramid.
Any convex 4-polytope can be divided into polyhedral pyramids by adding an interior point and creating one pyramid from each facet to the center point. This can be useful for computing volumes.