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TruncatedPolyhedron
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TruncatedPolyhedron

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gives the truncated polyhedron of poly by truncating all vertices.

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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

open allclose all

Basic Examples  (2)Summary of the most common use cases

Truncated polyhedron of a dodecahedron:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-chb4nx
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-pr69di
Out[2]=2

Find the truncated polyhedron of the Space Shuttle:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-ierreq

Visualization:

In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-7a6a3d
Out[2]=2

Scope  (4)Survey of the scope of standard use cases

TruncatedPolyhedron works on polyhedra:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-cpw0pk
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-nc5g0k
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-jmbj0g
Out[3]=3

TruncatedPolyhedron of Platonic solids includes Tetrahedron:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-3o58n0
Out[1]=1

Cube:

In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-ruxc6r
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-umhlf3
Out[3]=3

Dodecahedron:

In[4]:=4
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-frlodk
Out[4]=4

Octahedron:

In[5]:=5
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-glsvr6
Out[5]=5

Icosahedron:

In[6]:=6
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-gdp0ug
Out[6]=6

Support polyhedron meshes:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-3cfo8t
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-g06evt
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-pu5sqi
Out[3]=3

Truncate the polyhedron by different length ratios:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-e1thk8
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-efawwl
Out[2]=2

Applications  (9)Sample problems that can be solved with this function

Basic Applications  (3)

Gallery of Platonic solids and their truncated polyhedra:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-bq5o9d
Out[1]=1

Gallery of Archimedean solids and their truncated polyhedra:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-7ce8cn
Out[1]=1

Truncated compounds of Platonic solids:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-hkjz9t
Out[1]=1

Archimedean solids:

In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-y54rsb
Out[2]=2

Polyhedron Operations  (6)

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

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-0iw9f4
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-01o7bm
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-fzzeia
Out[3]=3

Needle operation:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-stfdpv
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-1v7nqw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-xckcgm
Out[3]=3

Join operation:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-h4ouo7
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-kn06zl
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-22wg6p
Out[3]=3

Bevel operation:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-k4v1d
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-wk7pax
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-z525zx
Out[3]=3

Expand operation:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-gibvuz
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-ewk0ci
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-birkfg
Out[3]=3

Ortho operation:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-nutc2o
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-46o46h
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-wni3ro
Out[3]=3

Properties & Relations  (2)Properties of the function, and connections to other functions

The truncated simple polyhedron is simple:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-r62rjj
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-guy1qu
Out[2]=2

The truncated convex polyhedron is convex:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-goye1v
In[2]:=2
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-zl6aq7
Out[2]=2

Possible Issues  (2)Common pitfalls and unexpected behavior

TruncatedPolyhedron only supports simple polyhedra:

In[1]:=1
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-lqo9mg
In[2]:=2
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https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-388cdr
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-rtw2bh
Out[3]=3

TruncatedPolyhedron can return degenerate polyhedra:

In[1]:=1
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-ozqw29
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-526pxv
Out[2]=2

Neat Examples  (1)Surprising or curious use cases

Truncate a tetrahedron:

In[1]:=1
✖
https://wolfram.com/xid/08dxmcc0djgvdk9lnkyj2-1vgvc2
Out[1]=1
Wolfram Research (2019), TruncatedPolyhedron, Wolfram Language function, https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html.
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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.

✖
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.

✖
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

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

BibTeX

@misc{reference.wolfram_2025_truncatedpolyhedron, author="Wolfram Research", title="{TruncatedPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}", note=[Accessed: 12-May-2025 ]}

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@misc{reference.wolfram_2025_truncatedpolyhedron, author="Wolfram Research", title="{TruncatedPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}", note=[Accessed: 12-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_truncatedpolyhedron, organization={Wolfram Research}, title={TruncatedPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}, note=[Accessed: 12-May-2025 ]}

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@online{reference.wolfram_2025_truncatedpolyhedron, organization={Wolfram Research}, title={TruncatedPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/TruncatedPolyhedron.html}, note=[Accessed: 12-May-2025 ]}