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1. Elementary symmetry question
I 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.
2. Re: Elementary symmetry question
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
3. Re: Elementary symmetry question
(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
What sixth form subject includes symmetry of this type?
4. Re: Elementary symmetry question
(Original post by grazie)
What sixth form subject includes symmetry of this type?
sorry. you are quite right. I mis-labelled this one.
5. Re: Elementary symmetry question
(Original post by Plato's Trousers)
sorry. you are quite right. I mis-labelled this one.
You can edit the label from the first post.
6. Re: Elementary symmetry question
(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
page 5
7. Re: Elementary symmetry question
(Original post by sputum)
page 5
Thanks, but this is a regular tetrahedron, not a triangular prism.
8. Re: Elementary symmetry question
(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 owe you a favour..

I can't absolutely guarantee its correctness but I tried.
Last edited by BabyMaths; 11-07-2012 at 10:57.
9. Re: Elementary symmetry question
(Original post by BabyMaths)
I owe you a favour..

I can't absolutely guarantee its correctness but I tried.
ooh! Thanks. Can you just tell me which symmetries are which?
10. Re: Elementary symmetry question
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.
Last edited by BabyMaths; 11-07-2012 at 11:27.
11. Re: Elementary symmetry question
(Original post by Plato's Trousers)
I know I am being dumb here.
(Original post by Plato's Trousers)
Thanks, but this is a regular tetrahedron, not a triangular prism.
blech

sorry to one-up you on the dumbness front
12. Re: Elementary symmetry question
(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.
cool. thanks

(Original post by sputum)
blech

sorry to one-up you on the dumbness front
he he. np
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