
#1
Aug407, 07:42 AM

P: 8

Hello,
in my Book is a formula, namely sigma^(1) C_2 = sigma^(12) where sigma^(1) is a reflection about the xzplane, C_2 is a pirotation about the zaxis and sigma^(12) is a reflection about the midway plane between xz and yzplane. When i in my Imagination make the steps on the left I come out at a totally different point as where the righthand side would send me. Obviously I have completely misunderstood the formula and I don't the the sun anymore. Can someone please explain me the meaning of that statement? Thanks alot 



#2
Aug407, 09:53 AM

Sci Advisor
HW Helper
P: 4,301

Consider a unit cube and label its corners 1 through 6. Then you can write down how the symmetries act on these corners as a permutation.
Also, note that there is no general consensus on the order of the operations, some people mean "first do [itex]\sigma^1[/itex] then [itex]C_2[/itex]" when they write down [itex]\sigma^1 C_2[/itex], some people read it as "perform [itex]\sigma^1[/itex] after [itex]C_2[/itex]". Maybe this is why you don't get the same answer? Alternatively, you could write out the operations as matrices working on the vectors of a standard orthonormal basis and work out the left hand side by matrix multiplication. 



#3
Aug407, 09:59 AM

Emeritus
Sci Advisor
PF Gold
P: 11,154

Either it's wrong or there's some error in transcribing it. The LHS is equivalent to a reflection about the yz plane.
Can you include the complete excerpt from the book  this will provide some context and make it possible to debug. Also include the name and edition of the book. The connection between the above operations and the symmetry group in the title (D2h) is also not clear. 



#4
Aug407, 02:56 PM

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