Elementary symmetry question
Maths and statistics discussion, revision, exam and homework help.
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Elementary symmetry questionI know I am being dumb here. The triangular prism (two equilateral triangle faces, three square faces) has 12 symmetries. I can only find 10!
identity
3 rotations through pi (exchanging triangular faces)
2 rotations through 2/3 pi (exchanging square faces)
3 reflections in planes perp to the triangular faces
1 reflection in plane parallel to the triangular faces
that's 10. what are the other two??
EDIT:
Duhh... got it. the other two are composites of rotations and reflection
Last edited by Plato's Trousers; 10-07-2012 at 17:11. -
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Re: Elementary symmetry questionWhat sixth form subject includes symmetry of this type?(Original post by Plato's Trousers)
actually, if anyone has a Cayley table for this group, I'd be really grateful. Can't find on anywhere and 12x12 takes a while to create -
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Re: Elementary symmetry questionsorry. you are quite right. I mis-labelled this one.(Original post by grazie)
What sixth form subject includes symmetry of this type? -
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Re: Elementary symmetry questionYou can edit the label from the first post.(Original post by Plato's Trousers)
sorry. you are quite right. I mis-labelled this one. -
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Re: Elementary symmetry questionpage 5(Original post by Plato's Trousers)
actually, if anyone has a Cayley table for this group, I'd be really grateful. Can't find on anywhere and 12x12 takes a while to create -
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Re: Elementary symmetry questionI owe you a favour..(Original post by Plato's Trousers)
actually, if anyone has a Cayley table for this group, I'd be really grateful. Can't find on anywhere and 12x12 takes a while to create
I can't absolutely guarantee its correctness but I tried.Last edited by BabyMaths; 11-07-2012 at 10:57. -
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Re: Elementary symmetry questionooh! Thanks. Can you just tell me which symmetries are which?(Original post by BabyMaths)
I owe you a favour..
I can't absolutely guarantee its correctness but I tried. -
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Re: Elementary symmetry questionr1 and r2 are rotations.
r3, r4 and r5 are the other rotations.
p1, p2, p3 are reflections.
p4 is the other reflection.
c1 is p4 followed by r1.
c2 is p4 followed by r2.
Edit: Thanks for the rep.
Last edited by BabyMaths; 11-07-2012 at 11:27. -
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Re: Elementary symmetry question(Original post by Plato's Trousers)
I know I am being dumb here.blech(Original post by Plato's Trousers)
Thanks, but this is a regular tetrahedron, not a triangular prism.
sorry to one-up you on the dumbness front
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Re: Elementary symmetry questioncool. thanks(Original post by BabyMaths)
r1 and r2 are rotations.
r3, r4 and r5 are the other rotations.
p1, p2, p3 are reflections.
p4 is the other reflection.
c1 is p4 followed by r1.
c2 is p4 followed by r2.
Edit: Thanks for the rep.
he he. np
