Symmetry of tetrahedron that is not a reflection nor a rotation
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.
- I cannot visualise this, as I keep ending up in some kind of rotation or reflection.
- Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.
symmetry
add a comment |Â
up vote
0
down vote
favorite
Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.
- I cannot visualise this, as I keep ending up in some kind of rotation or reflection.
- Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.
symmetry
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.
- I cannot visualise this, as I keep ending up in some kind of rotation or reflection.
- Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.
symmetry
Studying a tetrahedron I have identified twelve rotational symmetries and twelve reflectional symmetries. Now I am asked to identify a symmetry that is not a reflection nor a rotation, but which is equal to the product of three reflections.
- I cannot visualise this, as I keep ending up in some kind of rotation or reflection.
- Neither do I understand how a symmetry can occur without using a reflection or rotation as I only imagine displacements composed of these permutations.
symmetry
asked Aug 16 at 9:51
H. Vabri
62
62
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18
add a comment |Â
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2884609%2fsymmetry-of-tetrahedron-that-is-not-a-reflection-nor-a-rotation%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Since each symmetry necessarily permutes the vertices there are at most $4!=24$ symmetries (including the identity). You have found $24$; hence there are no more. In particular, any symmetry has to be a rotation or a reflection.Therefore, a product of symmetries is again a rotation or a reflection.
â Christian Blatter
Aug 16 at 10:17
There're rotoreflection and inversion operation. See more in Tetrahedral symmetry.
â Ng Chung Tak
Aug 16 at 10:18