Function Repository Resource:

PolyhedronFaceReflect

Reflect a polyhedron over a given face

Contributed by: Ed Pegg Jr
 ResourceFunction["PolyhedronFaceReflect"][polyhedron,k] reflects polyhedron over its kth face.

Details

The polyhedron can be given as a Polyhedron object containing a list of vertices and a list of vertex indices.

Examples

Basic Examples (3)

In the octahedron given below, a list of vertices is followed by a list of faces (vertex indices):

 In[1]:=

Reflect the octahedron over its first face:

 In[2]:=
 Out[2]=

Make a ring of eight octahedra:

 In[3]:=
 Out[3]=

Scope (2)

Reflect a dodecahedron over its first face:

 In[4]:=
 Out[5]=

Reflect the snub disphenoid over its fifth face:

 In[6]:=
 Out[7]=

Neat Examples (3)

Make a perfect ring of twelve 4-antiprisms:

 In[8]:=
 Out[9]=

Make a spiral of tetrahedra (the Boerdijk–Coxeter helix):

 In[10]:=
 Out[10]=

Compare with the result of TetrahelixMesh:

 In[11]:=
 Out[11]=

Make a chain of icosahedra:

 In[12]:=
 Out[12]=

Version History

• 1.0.0 – 31 January 2022