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 half‐planes HalfPlane[{p1,p2},v] and HalfPlane[{p1,p2},w].

Examples

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Basic Examples  (1)

The angle between the half‐planes:

Scope  (2)

Use DihedralAngle to find the angle between two half‐planes:

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[ℛ,{p1,p2}], where v and w are vectors in adjacent faces of {p1,p2} in a polyhedron ℛ:

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_2025_dihedralangle, author="Wolfram Research", title="{DihedralAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DihedralAngle.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_dihedralangle, organization={Wolfram Research}, title={DihedralAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/DihedralAngle.html}, note=[Accessed: 21-February-2025 ]}