SymPy | Polyhedron.rotate() in Python

SymPy | Polyhedron.pgroup() in Python

Last Updated : 27 Aug, 2019

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)])

SymPy | Polyhedron.rotate() in Python

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