Wedge (geometry)

In solid geometry, a wedge is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices.

A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge.^[1] . A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms;^[2] the wedge is an example of prismatoid because of its top edge is parallel to the rectangular base.^[3] The volume of a wedge is $${\displaystyle V=bh\left({\frac {a}{3}}+{\frac {c}{6}}\right),}$${\displaystyle V=bh\left({\frac {a}{3}}+{\frac {c}{6}}\right),} where the base rectangle is ${\displaystyle a}${\displaystyle a} by ${\displaystyle b}${\displaystyle b}, ${\displaystyle c}${\displaystyle c} is the apex edge length parallel to ${\displaystyle a}${\displaystyle a}, and ${\displaystyle h}${\displaystyle h} is the height from the base rectangle to the apex edge.^[1]

In some special cases, the wedge is the right prism if all edges connecting triangles are equal in length, and the triangular faces are perpendicular to the rectangular base.^[3]

Wedges can be created from decomposition of other polyhedra. For instance, the dodecahedron can be divided into a central cube with 6 wedges covering the cube faces. The orientations of the wedges are such that the triangle and trapezoid faces can connect and form a regular pentagon.

Two obtuse wedges can be formed by bisecting a regular tetrahedron on a plane parallel to two opposite edges.

• Weisstein, Eric W. "Wedge". MathWorld .

• Polyhedra
• Prismatoid polyhedra

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• Short description matches Wikidata