# DualPolyhedron

DualPolyhedron[poly]

gives the dual polyhedron of the polyhedron poly.

# Details and Options

• DualPolyhedron is also known as reciprocal or topological dual polyhedron.
• DualPolyhedron generates a Polyhedron with vertex points corresponding to faces of poly and edges corresponding to edges between faces of poly.
• A typical choice for the vertex points of the dual polyhedron is to use the centroid from each face of poly.
• DualPolyhedron takes the same options as Polyhedron.
• ## List of all options

•  VertexColors Automatic vertex colors to be interpolated VertexNormals Automatic effective vertex normals for shading VertexTextureCoordinates None coordinates for textures

# Examples

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## Basic Examples(2)

Dual polyhedron of a dodecahedron:

Find the dual of the space shuttle:

Visualization:

## Scope(3)

DualPolyhedron works on polyhedrons:

DualPolyhedron of Platonic solids includes Tetrahedron:

Cube:

Special polyhedron representations:

## Applications(9)

### Basic Applications(3)

Create a gallery of Platonic solids and their duals:

Create a gallery of Archimedean solids and their duals:

Dual compounds of Platonic solids:

Archimedean solids:

### Polyhedron Operations(6)

Use DualPolyhedron to compute the polyhedron operations, such as needle operation:

Meta-operation:

Join operation:

Zip operation:

Ortho operation:

Expand operation:

## Properties & Relations(4)

The dual of a simple polyhedron is simple:

The dual of a Platonic solid polyhedron is Platonic solid:

The dual of its dual is the original polyhedron:

Pyramids are self-dual polyhedrons:

## Possible Issues(3)

DualPolyhedron only supports simple polyhedra:

The dual of a polyhedron is topologically dual:

The dual of a dual:

DualPolyhedron can return degenerate polyhedra:

Wolfram Research (2019), DualPolyhedron, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPolyhedron.html.

#### Text

Wolfram Research (2019), DualPolyhedron, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPolyhedron.html.

#### CMS

Wolfram Language. 2019. "DualPolyhedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DualPolyhedron.html.

#### APA

Wolfram Language. (2019). DualPolyhedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DualPolyhedron.html

#### BibTeX

@misc{reference.wolfram_2023_dualpolyhedron, author="Wolfram Research", title="{DualPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DualPolyhedron.html}", note=[Accessed: 22-September-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_dualpolyhedron, organization={Wolfram Research}, title={DualPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/DualPolyhedron.html}, note=[Accessed: 22-September-2023 ]}