Function Repository Resource:

PolyhedronFaceReflect

Source Notebook

Reflect a polyhedron over a given face

Contributed by: Ed Pegg Jr

ResourceFunction["PolyhedronFaceReflect"][polyhedron,k]

reflects polyhedron over its k^th 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]:=

octa = Polyhedron[{{-1, 0, 0}, {0, -1, 0}, {0, 0, -1}, {0, 0, 1}, {0, 1, 0}, {1, 0, 0}}, {{1, 2, 4}, {1, 3, 2}, {1, 4, 5}, {1, 5, 3}, {2, 3, 6}, {2, 6, 4}, {3, 5, 6}, {4, 6, 5}}];

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]:=

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Neat Examples (3)

Make a perfect ring of twelve 4-antiprisms:

In[8]:=

$anti4 = Polyhedron[{{1, -1, Root[-1 + 2 #^4& , 1, 0]}, {-1, -1, Root[-1 + 2 #^4& , 1, 0]}, {-1, 1, Root[-1 + 2 #^4& , 1, 0]}, {1, 1, Root[-1 + 2 #^4& , 1, 0]}, {2^Rational[1, 2], 0, Root[-1 + 2 #^4& , 2, 0]}, {0, 2^Rational[1, 2], Root[-1 + 2 #^4& , 2, 0]}, {-2^Rational[1, 2], 0, Root[-1 + 2 #^4& , 2, 0]}, {0, -2^Rational[1, 2], Root[-1 + 2 #^4& , 2, 0]}}, {{1, 2, 3, 4}, {5, 6, 7, 8}, {1, 8, 2}, { 2, 7, 3}, {3, 6, 4}, {4, 5, 1}, {1, 5, 8}, {2, 8, 7}, {3, 7, 6}, { 4, 6, 5}}]; Graphics3D[ FoldList[ResourceFunction["PolyhedronFaceReflect"], anti4, {10, 1, 8, 9, 1, 7, 8, 1, 10, 7, 1}], Boxed -> False]$