# DihedralAngle

DihedralAngle[{p1,p2},{v,w}]

gives the angle between two half-planes bounded by the line through p1 and p2 and extended in the direction v and w.

# Details

• DihedralAngle is also known as face angle or torsion angle.
• DihedralAngle[{p1,p2},{v,w}] is the length of the arc of the unit circle Circle[p1] on the plane with normal p2-p1 and delimited by the halfplanes HalfPlane[{p1,p2},v] and HalfPlane[{p1,p2},w].

# Examples

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## Basic Examples(1)

The angle between the halfplanes:

## Scope(2)

Use DihedralAngle to find the angle between two halfplanes:

DihedralAngle works with numeric arguments:

Symbolic arguments:

## Applications(1)

Torsion angle in chloral:

Torsion angle in a chain of atoms Cl-C-C-O:

## Properties & Relations(2)

Dihedral angle is the planar angle in the plane defined by the normal p2-p1 and a point p1.

DihedralAngle[{p1,p2},{v,w}] is equivalent to PolyhedronAngle[,{p1,p2}], where v and w are vectors in adjacent faces of {p1,p2} in a polyhedron :

## Possible Issues(1)

DihedralAngle gives generic values for symbolic parameters:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_dihedralangle, author="Wolfram Research", title="{DihedralAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DihedralAngle.html}", note=[Accessed: 04-October-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_dihedralangle, organization={Wolfram Research}, title={DihedralAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/DihedralAngle.html}, note=[Accessed: 04-October-2023 ]}