Tetrahedron
Overview
In geometry
, a tetrahedron (plural: tetrahedra) is a polyhedron
composed of four triangular
faces, three of which meet at each vertex
. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solid
s. The tetrahedron is the only convex polyhedron
that has four faces.
The tetrahedron is the three-dimensional case of the more general concept of a Euclidean
simplex
.
The tetrahedron is one kind of pyramid
, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point.
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 tetrahedron (plural: tetrahedra) is a polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
composed of four triangular
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
faces, three of which meet at each vertex
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
s. The tetrahedron is the only convex polyhedron
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...
that has four faces.
The tetrahedron is the three-dimensional case of the more general concept of a Euclidean
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
.
The tetrahedron is one kind of 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....
, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point.