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Function Repository Resource:

TetrahedronEdgeAngles

Source Notebook

Given edgelengths of a tetrahedron, return the dihedral angles opposite those edges

Contributed by: Wolfram Staff

ResourceFunction["TetrahedronEdgeAngles"][{a,b,c, d, e, f}]

returns the angles opposite edges (a,b,c,d,e,f).

Examples

Basic Examples

Here is a rare tetrahedron where all dihedral angles are nice:

In[1]:=
ResourceFunction[
 "TetrahedronEdgeAngles"][{2, 2 Sqrt[2], Sqrt[3], 2, Sqrt[3], Sqrt[
  3]}]
Out[1]=

A set of vertices for the above tetrahedron:

In[2]:=
vert = {{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {1, 1, 1}}; 
EuclideanDistance @@ # & /@ Subsets[vert, {2}]
Out[2]=

Opposing edges are 1-6, 2-5 and 3-4:

In[3]:=
Subsets[{w, x, y, z}, {2}]
Out[3]=

Usually the angles are messier:

In[4]:=
ResourceFunction["TetrahedronEdgeAngles"][{3, 4, 5, 11, 2, 13}^(1/2)]
Out[4]=

Scope

Another tetrahedron with nicer angles:

In[5]:=
ResourceFunction["TetrahedronEdgeAngles"][{2, 3, 6, 5, 8, 9}^(1/2)]
Out[5]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

License Information