dihedron

A degenerate 4-dimensional case exists as 3-sphere tiling, a tetrahedral dihedron.

Therefore it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group.

A dihedron is a type of polyhedron, made of two polygon faces which share the same set of edges.

Regular dihedron examples: (spherical tilings)

(Two half-plane tiles, infinite dihedron)

The dual of a n-gonal dihedron is the n-gonal hosohedron, where n digon faces share two vertices.

A dihedron can be considered a degenerate prism consisting of two (planar) n-sided polygons connected "back-to-back", so that the resulting object has no depth.

In geometry, an order-2 apeirogonal tiling or apeirogonal dihedron is a tiling of the plane consisting of two apeirogons.

Danish Pavilion: designed by Tyge Hvass, this was a dihedron of reddish wood with a gabled roof, evoking a typical Danish mountain house.

As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering the sphere, each face being a hemisphere, and vertices around a great circle.

In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q).