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


  • 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].


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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:

Introduced in 2019