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# What is a dual?

Updated: 10/24/2022

Wiki User

13y ago

A dual is almost like the opposite of a given polytope. For example, a regular octahedron is the dual of a cube.

Look at the similarities between duals with the example of a cube and regular octahedron:

Cube:

Vertices: 8

Edges: 12

Faces: 6

Edges per vertex: 3

Type of face: square (4-sided)

Regular Octahedron:

Vertices: 6

Edges: 12

Faces: 8

Edges per vertex: 4

Type of face: triangle (3-sided)

Both of these shapes can be put together to form a compound and can be rectified to form the same new shape: a cuboctahedron.

Also, duals can fit perfectly inside another where each edge touches the face of the other.

In this same way a regular dodecahedron is the dual of a regular icosahedron. Some polyhedra like the regular tetrahedron is the dual of itself. All polyhedra have duals. Polygons, polychora, and other polytopes can also have duals in a similar fashion.

Wiki User

13y ago

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