When studying the dihedral group of a square, do we consider only vertices or the whole points which the...
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When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers? Because the vertices of square also gives the same symmetries.
symmetry
edited Dec 28 '18 at 15:01
Blue
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
$endgroup$
add a comment |
$begingroup$
When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers? Because the vertices of square also gives the same symmetries.
symmetry
edited Dec 28 '18 at 15:01
Blue
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
$endgroup$
1
$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
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– user629838
Dec 28 '18 at 14:53
add a comment |
$begingroup$
When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers? Because the vertices of square also gives the same symmetries.
symmetry
edited Dec 28 '18 at 15:01
Blue
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
$endgroup$
When studying the dihedral group of a square, do we consider only vertices or the whole points which the square covers? Because the vertices of square also gives the same symmetries.
symmetry
symmetry
edited Dec 28 '18 at 15:01
Blue
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
edited Dec 28 '18 at 15:01
Blue
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
edited Dec 28 '18 at 15:01
Blue
48.5k870154
edited Dec 28 '18 at 15:01
Blue
48.5k870154
edited Dec 28 '18 at 15:01
Blue
48.5k870154
48.5k870154
asked Dec 28 '18 at 14:49
user629838user629838
11
asked Dec 28 '18 at 14:49
user629838user629838
11
asked Dec 28 '18 at 14:49
user629838user629838
11
11
1
$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
$endgroup$
– user629838
Dec 28 '18 at 14:53
add a comment |
1
$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
$endgroup$
– user629838
Dec 28 '18 at 14:53
1
1
$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
$endgroup$
– user629838
Dec 28 '18 at 14:53
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
$endgroup$
– user629838
Dec 28 '18 at 14:53
add a comment |
1 Answer
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$begingroup$
When studying the symmetry groups of a whole geometric object, the symmetry of all points of that object is considered.
Take e.g. a square that contains a non-symmetric pattern on its surface: it has a different symmetry group than a square: its symmetry group is the identity group.
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
$endgroup$
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
add a comment |
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1 Answer
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$begingroup$
When studying the symmetry groups of a whole geometric object, the symmetry of all points of that object is considered.
Take e.g. a square that contains a non-symmetric pattern on its surface: it has a different symmetry group than a square: its symmetry group is the identity group.
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
$endgroup$
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
add a comment |
$begingroup$
When studying the symmetry groups of a whole geometric object, the symmetry of all points of that object is considered.
Take e.g. a square that contains a non-symmetric pattern on its surface: it has a different symmetry group than a square: its symmetry group is the identity group.
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
$endgroup$
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
add a comment |
$begingroup$
When studying the symmetry groups of a whole geometric object, the symmetry of all points of that object is considered.
Take e.g. a square that contains a non-symmetric pattern on its surface: it has a different symmetry group than a square: its symmetry group is the identity group.
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
$endgroup$
When studying the symmetry groups of a whole geometric object, the symmetry of all points of that object is considered.
Take e.g. a square that contains a non-symmetric pattern on its surface: it has a different symmetry group than a square: its symmetry group is the identity group.
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
edited Jan 1 at 20:31
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
answered Dec 28 '18 at 16:53
IV_IV_
1,345525
1,345525
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
add a comment |
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
$begingroup$
Can you elaborate please
$endgroup$
– user629838
Jan 1 at 17:25
add a comment |
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$begingroup$
You seem to be answering your own question. The set of vertices of the square has the same symmetries as the whole set of points of the square. Or perhaps I misunderstand your question?
$endgroup$
– Pierre-Guy Plamondon
Dec 28 '18 at 14:51
$begingroup$
Absolutely but which set do we consider in dihedral group of order 8
$endgroup$
– user629838
Dec 28 '18 at 14:53