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.
Asked
Active
Viewed 50 times
0
-
1You 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? – Pierre-Guy Plamondon Dec 28 '18 at 14:51
-
Absolutely but which set do we consider in dihedral group of order 8 – user629838 Dec 28 '18 at 14:53
1 Answers
0
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.
IV_
- 6,964