WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

PolyhedronAngle
✖
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

open allclose all

Basic Examples  (2)Summary of the most common use cases

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

In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-6kgxf4
In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-vd2lvt
Out[3]=3

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

In[1]:=1
✖
https://wolfram.com/xid/0d4j4ks30or21nli-9lo0fb
In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-bylpse
Out[2]=2

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

In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-sbbhax
Out[3]=3

Scope  (2)Survey of the scope of standard use cases

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

In[1]:=1
✖
https://wolfram.com/xid/0d4j4ks30or21nli-n05why
In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-x01uu4
Out[2]=2

The dihedral angle at the given edge:

In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-lik5jn
Out[3]=3

PolyhedronAngle works on polyhedra:

In[1]:=1
✖
https://wolfram.com/xid/0d4j4ks30or21nli-jmil41
In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-we6lud
Out[2]=2

Tetrahedron:

In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-3o58n0
Out[3]=3

Octahedron:

In[4]:=4
✖
https://wolfram.com/xid/0d4j4ks30or21nli-ruxc6r
Out[4]=4

Properties & Relations  (2)Properties of the function, and connections to other functions

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:

In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-1q3mjj
In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-8q1d8a
In[5]:=5
✖
https://wolfram.com/xid/0d4j4ks30or21nli-k2pv8t
Out[5]=5
In[6]:=6
✖
https://wolfram.com/xid/0d4j4ks30or21nli-beub9c
Out[6]=6

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

In[1]:=1
✖
https://wolfram.com/xid/0d4j4ks30or21nli-r7mz30
In[2]:=2
✖
https://wolfram.com/xid/0d4j4ks30or21nli-4c1k1y
In[3]:=3
✖
https://wolfram.com/xid/0d4j4ks30or21nli-gk4ig3
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d4j4ks30or21nli-xxzp0h
Out[4]=4
Wolfram Research (2019), PolyhedronAngle, Wolfram Language function, https://reference.wolfram.com/language/ref/PolyhedronAngle.html.
✖
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.

✖
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.

✖
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

✖
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: 04-April-2025 ]}

✖
@misc{reference.wolfram_2025_polyhedronangle, author="Wolfram Research", title="{PolyhedronAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PolyhedronAngle.html}", note=[Accessed: 04-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: 04-April-2025 ]}

✖
@online{reference.wolfram_2025_polyhedronangle, organization={Wolfram Research}, title={PolyhedronAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/PolyhedronAngle.html}, note=[Accessed: 04-April-2025 ]}