The discussion revolves around the limitations of symmetry in geometry, particularly in relation to finite simple groups and their implications for 2D and 3D symmetrical geometric objects. Participants explore the nature of spatial symmetry within the confines of our three-dimensional world.
Participants express differing views on the implications of group theory for symmetry in geometry, indicating that multiple competing perspectives remain without a consensus.
The discussion touches on the relationship between group theory and geometric symmetry, but does not resolve the mathematical implications or the definitions of the sets involved.
Islam Hassan said: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 said: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.