| Cyclic Group | Symbol | Our Thoughts |
|---|---|---|
| C1 |  |
Things that have no reflection and no rotation are considered to be finite figures of order 1. One such example is the Franklin & Marshall College logo (nothing like plugging our own institution!). Therefore, the F&M logo is a finite figure of C1. |
| C2 |  |
With every refreshing sip of a cold Pepsi we see an example of a figure in the category C2. These figures cannot be reflected at all, but can be rotated by a half turn to return to the original figure. The only difficulty with the Pepsi symbol, however, is that it is of two colors. Only when the colors are ignored can we truly consider the figure a cyclic figure of order 2. |
| C3 |  |
Avery, an office supply company uses the symbol to the left. This triangular finite figure is a fine example of a cyclic figure of order 3 since it cannot be reflected along any line, but it can be rotated by sixty degrees to give the original object. |
| C4 |  |
The finite figure to the left was created by rotating the numeral 2 four times (each rotation is 90 degrees). Since the number 2 has no reflection, the entire figure has only rotation. Thus, the figure must be a cyclic figure of order 4 as long as color is not taken into account. |
| C7 |  |
The newest symbol for the Holiday Inn is a wonderful example of a cyclic figure of order seven. The figure is cyclic (disregarding color) since there is no reflection. It is easy to see that the figure must be rotated seven times to yield the original figure. |
| C8 |  |
For those of you who have visited the "Sweetest Place on Earth" (a.k.a. Hersheypark) know this symbol well. The finite figure that Hershey uses as a logo is a figure that can be rotated by 1/8 of a turn to give the original object as long as the colors are not taken into account. Like the other figures in this table, the logo cannot be reflected at all to give the original object. This figure can be categorized as C8. |
During our trip to Europe, we found many examples of cyclic groups. Please CLICK HERE to see our photos of cyclic groups.