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 vertex‐truncated 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.

    • List of all options

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:

Dodecahedron:

Octahedron:

Icosahedron:

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: 22-December-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: 22-December-2024 ]}