What is meant by point group symmetries of a cube?

[drennon236]

I am reading a paper related to microstructures, and it says a unit cell has geometric cubic symmetry. When I tried to google the meaning it said: "The symmetry group of a cube is isomorphic to S4, the permutation group on 4 elements." Which tells me basically nothing as this is not my field. Could anyone try to give me an alternate explanation to what is meant by point group symmetries of a cube?

tips/1_gprr6q.png]

 

[dik]

does this help?

https://en.wikipedia.org/wiki/Cubic_crystal_system#Crystal_classes

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-Dik

 

[drennon236]

Honestly, no

 

[IRstuff]

OP's reference comes from

https://arxiv.org/pdf/2012.01359.pdf

which says

(c) Illustration of geometric cubic symmetry. The repetitive domain in the microstructure: the region enclosed by the red bold lines.

So 8 repetitive domains per face and 6 faces ...

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[dik]

Thanks, IRS...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[drennon236]

I think I get it now, by operations of symmetry a cube can be built from the highlighted figure in (c).