PolyhedronAngle

PolyhedronAngle[poly,p]

gives the solid angle at the point p and spanned by edges with common point p.

PolyhedronAngle[poly,e]

gives the dihedral angle between the two faces with common edge e.

Details

Examples

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Basic Examples  (2)

The dihedral angle between two faces with common edge {1,2} of ℛ in canonical form:

The solid angle at the vertex point {0,0,0} and spanned by edges:

The solid angle of ℛ at the point 1 in canonical form:

Scope  (2)

Use PolyhedronAngle to find the solid angles at the vertex points:

The dihedral angle at the given edge:

PolyhedronAngle works on polyhedra:

Tetrahedron:

Octahedron:

Properties & Relations  (2)

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

PolyhedronAngle[ℛ,p] is equivalent to SolidAngle[p,{u1,…,ud}] where u1,…,ud are vectors adjacent to the point p in a polyhedron ℛ:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_polyhedronangle, author="Wolfram Research", title="{PolyhedronAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronAngle.html}", note=[Accessed: 01-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_polyhedronangle, organization={Wolfram Research}, title={PolyhedronAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/PolyhedronAngle.html}, note=[Accessed: 01-April-2025 ]}