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## Homework Statement

"Show that the C5 group is not a crystal point group."

**2. Relevant information**

1) "There exists another type of symmetry operation, called point symmetry, which leaves a point in the structure invariant"

2) "In crystallography, the angle of rotation cannot be arbitrary but can only take the following fractions of 2*pi: THETA= 2*pi/n where n = 1,2,3,4,6"

## The Attempt at a Solution

So, the problem states that C5 is a group, mathematically, but just not a crystal point group. But obviously, C5 is also a point symmetry, since the point at the rotation axis is invariant. So the only thing I can think of is saying "by definition," because of the undemonstrated statement given by 2) above.

I have no idea how to proceed. I mean, it's a group. It's a point symmetry. If that's all I know, it should be a point group. Why isn't it a

*crystal*point group? My book never explains what technical meaning modifying a phrase by "crystal" would yield.

Any hints would be greatly appreciated.

Thanks.