Torus
✖
Torus
represents a torus centered at {x,y,z} with inner radius rinner and outer radius router.
Details and Options

- Torus is also known as torus of revolution.
- Torus can be used as a geometric region and a 3D graphics primitive.
- Torus[] is equivalent to Torus[{0,0,0},{1/2,1}].
- Torus represents the shell
.
- Torus can be used in Graphics3D.
- Graphics rendering is affected by directives such as FaceForm, Specularity, Opacity and color.

Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Scope (18)Survey of the scope of standard use cases
Graphics (9)
Specification (4)

https://wolfram.com/xid/0j41r02s-btz1q2

Filled tori with different outer radii:

https://wolfram.com/xid/0j41r02s-l0hn2

Filled tori with different inner radii:

https://wolfram.com/xid/0j41r02s-hky91r

Short form for a torus with radii at the origin:

https://wolfram.com/xid/0j41r02s-37iz6

Styling (4)

https://wolfram.com/xid/0j41r02s-cdxdbh

Different properties can be specified for the front and back of faces using FaceForm:

https://wolfram.com/xid/0j41r02s-vb6wx

Filled tori with different specular exponents:

https://wolfram.com/xid/0j41r02s-d1tyd0


https://wolfram.com/xid/0j41r02s-ca9zt

Opacity specifies the face opacity:

https://wolfram.com/xid/0j41r02s-v6995

Coordinates (1)
Regions (9)
Embedding dimension is the dimension of the space in which the torus lives:

https://wolfram.com/xid/0j41r02s-y220

Geometric dimension is the dimension of the shape itself:

https://wolfram.com/xid/0j41r02s-bx9tom


https://wolfram.com/xid/0j41r02s-c7lq97

https://wolfram.com/xid/0j41r02s-f70gib

Get conditions for point membership:

https://wolfram.com/xid/0j41r02s-inebf9


https://wolfram.com/xid/0j41r02s-se0twe

https://wolfram.com/xid/0j41r02s-e06l44


https://wolfram.com/xid/0j41r02s-gwq4b4


https://wolfram.com/xid/0j41r02s-oknxhk


https://wolfram.com/xid/0j41r02s-jcsb4b

https://wolfram.com/xid/0j41r02s-8aexdg

The equidistance contours for a torus:

https://wolfram.com/xid/0j41r02s-ew8anh


https://wolfram.com/xid/0j41r02s-kjgbyj

https://wolfram.com/xid/0j41r02s-zognbt


https://wolfram.com/xid/0j41r02s-d7g53y

https://wolfram.com/xid/0j41r02s-mtue

Nearest points to an enclosing sphere:

https://wolfram.com/xid/0j41r02s-e29k5d

https://wolfram.com/xid/0j41r02s-5ksoo8

https://wolfram.com/xid/0j41r02s-uv1cfm


https://wolfram.com/xid/0j41r02s-ypd96t


https://wolfram.com/xid/0j41r02s-po0eks


https://wolfram.com/xid/0j41r02s-dym4fu

https://wolfram.com/xid/0j41r02s-i3tfrr


https://wolfram.com/xid/0j41r02s-l3exhn


https://wolfram.com/xid/0j41r02s-23060u


https://wolfram.com/xid/0j41r02s-nf9ton

https://wolfram.com/xid/0j41r02s-hyz4dq

Solve equations in a torus region:

https://wolfram.com/xid/0j41r02s-bnrw6

https://wolfram.com/xid/0j41r02s-lhnpf3

Applications (2)Sample problems that can be solved with this function

https://wolfram.com/xid/0j41r02s-fp53yw

Use Torus to render nodes in a GraphPlot3D:

https://wolfram.com/xid/0j41r02s-u52ea

Properties & Relations (3)Properties of the function, and connections to other functions
An implicit specification of a torus generated by ContourPlot3D:

https://wolfram.com/xid/0j41r02s-be10oz

A parametric specification of a torus generated by ParametricPlot3D:

https://wolfram.com/xid/0j41r02s-i7028d

Torus is the RegionBoundary of FilledTorus:

https://wolfram.com/xid/0j41r02s-h6x47m

Wolfram Research (2021), Torus, Wolfram Language function, https://reference.wolfram.com/language/ref/Torus.html.
Text
Wolfram Research (2021), Torus, Wolfram Language function, https://reference.wolfram.com/language/ref/Torus.html.
Wolfram Research (2021), Torus, Wolfram Language function, https://reference.wolfram.com/language/ref/Torus.html.
CMS
Wolfram Language. 2021. "Torus." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Torus.html.
Wolfram Language. 2021. "Torus." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Torus.html.
APA
Wolfram Language. (2021). Torus. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Torus.html
Wolfram Language. (2021). Torus. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Torus.html
BibTeX
@misc{reference.wolfram_2025_torus, author="Wolfram Research", title="{Torus}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/Torus.html}", note=[Accessed: 09-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_torus, organization={Wolfram Research}, title={Torus}, year={2021}, url={https://reference.wolfram.com/language/ref/Torus.html}, note=[Accessed: 09-July-2025
]}