Wedge (geometry)

Overview

In solid geometry

Solid geometry

In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. It was developed following the development of plane geometry...

, a

**wedge**is a polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

defined by two triangle

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 ....

s and three trapezoid

Trapezoid

In Euclidean geometry, a convex quadrilateral with one pair of parallel sides is referred to as a trapezoid in American English and as a trapezium in English outside North America. A trapezoid with vertices ABCD is denoted...

faces. A wedge has five faces, nine edges, and six vertices.

A wedge is a subclass of the prismatoid

Prismatoid

In geometry, a prismatoid is a polyhedron where all vertices lie in two parallel planes....

s with the base and opposite ridge in two parallel planes.

A wedge can also be classified as a digon

Digon

In geometry, a digon is a polygon with two sides and two vertices. It is degenerate in a Euclidean space, but may be non-degenerate in a spherical space.A digon must be regular because its two edges are the same length...

al cupola

Cupola (geometry)

In geometry, a cupola is a solid formed by joining two polygons, one with twice as many edges as the other, by an alternating band of triangles and rectangles...

.

Wedges can be created from decomposition of other polyhedra. For instance, the dodecahedron can be divided into a central cube

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

with 6 wedges covering the cube faces.