# TruncatedPolyhedron

TruncatedPolyhedron[poly]

gives the truncated polyhedron of poly by truncating all vertices.

TruncatedPolyhedron[poly,l]

truncates the polyhedron poly by a length ratio l at its vertices.

# Details and Options

• TruncatedPolyhedron is also known as ambo polyhedron, rectified polyhedron or vertextruncated polyhedron.
• TruncatedPolyhedron generates a polyhedron from poly by cutting vertices by a length ratio l and creating a new face in place of each vertex.
• TruncatedPolyhedron takes the same options as Polyhedron.

# Examples

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## Basic Examples(2)

Truncated polyhedron of a dodecahedron:

Find the truncated polyhedron of the Space Shuttle:

Visualization:

## Scope(4)

TruncatedPolyhedron works on polyhedra:

TruncatedPolyhedron of Platonic solids includes Tetrahedron:

Cube:

Support polyhedron meshes:

Truncate the polyhedron by different length ratios:

## Applications(9)

### Basic Applications(3)

Gallery of Platonic solids and their truncated polyhedra:

Gallery of Archimedean solids and their truncated polyhedra:

Truncated compounds of Platonic solids:

Archimedean solids:

### Polyhedron Operations(6)

Use TruncatedPolyhedron to compute the polyhedron operations, such as ambo operation:

Needle operation:

Join operation:

Bevel operation:

Expand operation:

Ortho operation:

## Properties & Relations(2)

The truncated simple polyhedron is simple:

The truncated convex polyhedron is convex:

## Possible Issues(2)

TruncatedPolyhedron only supports simple polyhedra:

TruncatedPolyhedron can return degenerate polyhedra:

## Neat Examples(1)

Truncate a tetrahedron:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_truncatedpolyhedron, author="Wolfram Research", title="{TruncatedPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_truncatedpolyhedron, organization={Wolfram Research}, title={TruncatedPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}, note=[Accessed: 21-June-2024 ]}