Polyhedron.pgroup() : pgroup() is a sympy Python library function that returns the permutations of the polyhedra.
Syntax : sympy.combinatorics.Polyhedrons.Polyhedron.pgroup()
Return : permutations of the Polyhedron.
Code #1 : pgroup() Example – tetrahedron
# Python code explaining # SymPy.Polyhedron.pgroup() # importing SymPy libraries from sympy.combinatorics import Permutation, Cycle from sympy.combinatorics.polyhedron import tetrahedron, octahedron # Using from # sympy.combinatorics.polyhedron.Polyhedron.pgroup() # Creating Polyhedron a = tetrahedron.copy() print ("Polyhedron - pgroup form : ", a.pgroup) a.rotate(0) print ("\nPolyhedron - pgroup form : ", a.pgroup) |
Output :
Polyhedron – pgroup form : PermutationGroup([
(1 2 3),
(3)(0 1 2),
(0 3 2),
(0 3 1),
(0 1)(2 3),
(0 2)(1 3),
(0 3)(1 2)])Polyhedron – pgroup form : PermutationGroup([
(1 2 3),
(3)(0 1 2),
(0 3 2),
(0 3 1),
(0 1)(2 3),
(0 2)(1 3),
(0 3)(1 2)])
Code #2 : pgroup() Example – octahedron
# Python code explaining # SymPy.Polyhedron.pgroup() # importing SymPy libraries from sympy.combinatorics import Permutation, Cycle from sympy.combinatorics.polyhedron import tetrahedron, octahedron # Using from # sympy.combinatorics.polyhedron.Polyhedron.pgroup() # Creating Polyhedron a = octahedron.copy() print ("Polyhedron - pgroup form : ", a.pgroup) a.rotate(0) print ("\nPolyhedron - pgroup form : ", a.pgroup) |
Output :
Polyhedron – pgroup form : PermutationGroup([
(5)(1 2 3 4),
(0 4 5 2),
(0 1 5 3),
(0 1)(2 4)(3 5),
(0 2)(1 3)(4 5),
(0 3)(1 5)(2 4),
(0 4)(1 3)(2 5),
(0 5)(1 4)(2 3),
(0 5)(1 2)(3 4),
(0 4 1)(2 3 5),
(0 1 2)(3 4 5),
(0 2 3)(1 5 4),
(0 4 3)(1 5 2)])Polyhedron – pgroup form : PermutationGroup([
(5)(1 2 3 4),
(0 4 5 2),
(0 1 5 3),
(0 1)(2 4)(3 5),
(0 2)(1 3)(4 5),
(0 3)(1 5)(2 4),
(0 4)(1 3)(2 5),
(0 5)(1 4)(2 3),
(0 5)(1 2)(3 4),
(0 4 1)(2 3 5),
(0 1 2)(3 4 5),
(0 2 3)(1 5 4),
(0 4 3)(1 5 2)])
