SymPy | Polyhedron.pgroup() in Python

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)])