Tetrahedron

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a tetrahedron (pl.: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a <a href="/facts/Polyhedron/UC0p9FTF">polyhedron</a> composed of four triangular <a href="/facts/Face_(geometry)/T2E6BTU4">faces</a>, six straight <a href="/facts/Edge_(geometry)/3lFN6sEz">edges</a>, and four <a href="/facts/Vertex_(geometry)/ID3cea9z">vertices</a>. The tetrahedron is the simplest of all the ordinary <a href="/facts/Convex_polytope/2pRHcRgC">convex polyhedra</a>.
The tetrahedron is the <a href="/facts/Three-dimensional/KAqKWUbS">three-dimensional</a> case of the more general concept of a <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean</a> <a href="/facts/Simplex/0FCfNRN8">simplex</a>, and may thus also be called a 3-simplex.
The tetrahedron is one kind of <a href="/facts/Pyramid_(geometry)/fCXRgFwu">pyramid</a>, which is a polyhedron with a flat <a href="/facts/Polygon/yAq7RjPz">polygon</a> base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a <a href="/facts/Triangle/cRXUwsMn">triangle</a> (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid".
Like all <a href="/facts/Convex_polyhedra/2pRHcRgC">convex polyhedra</a>, a tetrahedron can be folded from a single sheet of paper. It has two such <a href="/facts/Net_(polyhedron)/lU8fmGJs">nets</a>.
For any tetrahedron there exists a sphere (called the <a href="/facts/Circumsphere/m6EPvP2E">circumsphere</a>) on which all four vertices lie, and another sphere (the <a href="/facts/Insphere/pmXqc630">insphere</a>) <a href="/facts/Tangent/sF0jH3EI">tangent</a> to the tetrahedron's faces.

Tetrahedron open-in-new

Tetrahedron