Function Repository Resource:

# SimplexOrientation

Get the orientation of a simplex

Contributed by: Richard Hennigan (Wolfram Research)
 ResourceFunction["SimplexOrientation"][simplex] returns the orientation of simplex. ResourceFunction["SimplexOrientation"][{simplex1,simplex2,…}] returns the orientation of simplices in the given complex.

## Details and Options

A simplex can be specified by any of the following:
 Point[v] a point Line[{v1,v2}] a line segment Triangle[{v1,v2,v3}] or Polygon[{v1,v2,v3}] a filled triangle Tetrahedron[{v1,v2,v3,v4}] a filled tetrahedron Simplex[{v1,v2,…,vn}] an n-1 dimensional simplex

## Examples

### Basic Examples (3)

Get the orientation of a simplex:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

Find the permutations of the vertices of a simplex that are equivalent to the original simplex:

 In[3]:=
 Out[3]=
 In[4]:=
 Out[4]=
 In[5]:=
 Out[5]=

Get orientations for a list of simplices:

 In[6]:=
 Out[6]=
 In[7]:=
 Out[7]=

### Scope (6)

SimplexOrientation works with Point:

 In[8]:=
 Out[8]=

SimplexOrientation works with Line:

 In[9]:=
 Out[9]=
 In[10]:=
 Out[10]=

SimplexOrientation works with Triangle:

 In[11]:=
 Out[11]=
 In[12]:=
 Out[12]=

SimplexOrientation works with Tetrahedron:

 In[13]:=
 Out[13]=
 In[14]:=
 Out[14]=

Visualize orientation using Graphics3D and FaceForm:

 In[15]:=
 In[16]:=
 Out[16]=

Simplices can have arbitrary expressions as vertices:

 In[17]:=
 Out[17]=

We can see that the cat-dog-bird simplex has the opposite orientation to the cat-bird-dog simplex:

 In[18]:=
 Out[18]=

### Properties and Relations (1)

Check the output of the three argument form of StandardSimplex:

 In[19]:=
 Out[19]=

## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.0.0 – 11 March 2019