# Wedge

Wedge Rank3
SpaceSpherical
Notation
Bowers style acronymWedge
Coxeter diagramox xx&#y
Elements
Faces2 isosceles triangles, 2 isosceles trapezoids, 1 rectangle
Edges1+2+2+4
Vertices2+4
Vertex figures2 isosceles triangles
4 scalene triangles
Measures (edge length 1)
Central density1
Related polytopes
ArmyWedge
RegimentWedge
DualNotch
ConjugateWedge
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryK2×I, order 4
ConvexYes
NatureTame

The wedge is a variant of the triangular prism with a base rectangle, opposite a top edge, with two isosceles triangles and two isosceles trapezoids as faces.

The term "wedge" can also be used generally to refer to any monostratic polytope with a sub-dimensional top base that is not a pyramid.

## In vertex figures

Variants of the wedge (with lateral edge lengths of 2) by changing the edge opposite of the square appear as the vertex figure of the uniform small rhombated pentachoron. With a top edge length of 2, it is the vertex figure of the uniform small rhombated tesseract, and with a top edge length of (1+5)/2, it is the vertex figure of the uniform small rhombated hecatonicosachoron. By changing the base edges perpendicular to the top edge instead, it appears as the vertex figure of the uniform small rhombated hexacosichoron.

Variants of the wedge by changing the two edges parallel to the top edge appear as the vertex figure of the nonuniform rectified decachoron, with edge lengths of 3 for the aforementioned edges, and the nonuniform rectified tetracontoctachoron, with edge lengths of 2+2 for the aforementioned edges, with both having no corealmic realization.

Including nonconvex cases, the wedge appears as a vertex figure of a total of 23 uniform polychora, commonly known as the sphenovert polychora.

Variants of the wedge (with base-parallel edge lengths of 2) by changing the edge opposite to the square appear as the vertex figure of the nonuniform rectified n-gonal duoprisms, and has no corealmic realization.