Is Symmetry Limited in Geometry?

[Islam Hassan]

Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D symmetrical geometric objects/arrangement is limited?

Is spatial symmetry limited in our 3D world?


IH

 

[chiro]

Given the complete classification of finite simple groups, can one say that the number of all conceivable 2D/3D symmetrical geometric objects/arrangement is limited?

Is spatial symmetry limited in our 3D world?

IH

Hello Islam Hassan and welcome to the forums.

The question that I have to ask that comes to mind is what the cardinality of the sets themselves involved in the groups you are talking about?

I don't know that much about group theory (finite or otherwise) but I do know that the sets relating to the associated groups you are referring to are going to have some kind of relation to your answer.

 

[Islam Hassan]

Hello Islam Hassan and welcome to the forums.

The question that I have to ask that comes to mind is what the cardinality of the sets themselves involved in the groups you are talking about?

I don't know that much about group theory (finite or otherwise) but I do know that the sets relating to the associated groups you are referring to are going to have some kind of relation to your answer.

I believe that the sets involved may be both finite and infinite; one category of finite simple group in the classification theorem are simple groups of Lie type which, if I recall correctly, can have an infinite number of elements.


IH

 

[M Quack]

The answer is known for periodic structures where a "unit cell" is repeated to form an infinite 2D or 3D lattice.

The application in physics is crystallography.