Other Objects
A perfect snowflake would have *66 symmetry, |
The pentagon has symmetry *55, the whole image with arrows 55. |
The Flag of Hong Kong has 5 fold rotation symmetry, 55. |
The symmetry of a 2D object without translational symmetry can be described by the 3D symmetry type by adding a third dimension to the object which does not add or spoil symmetry. For example, for a 2D image we can consider a piece of carton with that image displayed on one side; the shape of the carton should be such that it does not spoil the symmetry, or it can be imagined to be infinite. Thus we have nn and *nn.
Similarly, a 1D image can be drawn horizontally on a piece of carton, with a provision to avoid additional symmetry with respect to the line of the image, e.g. by drawing a horizontal bar under the image. Thus the discrete symmetry groups in one dimension are 11, *11, ∞∞ and and *∞∞.
Another way of constructing a 3D object from a 1D or 2D object for describing the symmetry is taking the Cartesian product of the object and an asymmetric 2D or 1D object, respectively.
Read more about this topic: Orbifold Notation
Famous quotes containing the word objects:
“I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way. But in this water there are countless objects at different depths; and certain influences will give certain kinds of those objects an upward influence which may be intense enough and continue long enough to bring them into the upper visible layer. After the impulse ceases they commence to sink downwards.”
—Charles Sanders Peirce (1839–1914)
“I was afraid that by observing objects with my eyes and trying to comprehend them with each of my other senses I might blind my soul altogether.”
—Socrates (469–399 B.C.)