How to evaluate a symmetry rank:
A symmetry rank is a number of possible symmetry operations which can be performed
in order to match the figure with itself.
A square has the highest possible rank. It can be self-matched in four different ways
using reflection operations - from top to bottom, from left to right, and in two diagonal
directions.
It also can be self-matched by rotating it around it's center in three different angles -
90, 180, and 270 degrees. Rotation in 360 or more degrees and negative degrees are considered illegal.
So we can say that the square's symmetry rank is 7.
This simple table will help you estimate the symmetry rank of your configuration:
| Your figure's name | YourFigureName |
| Reflection from top to bottom | Yes (No) |
| Reflection from left to right | Yes (No) |
| Reflection from left bottom to right top | Yes (No) |
| Reflection from left top to right bottom | Yes (No) |
| Rotation by 90 degrees | Yes (No) |
| Rotation by 180 degrees | Yes (No) |
| Rotation by 270 degrees | Yes (No) |
| Symmetry Rank | Number of "Yes" |
Examples:
For a rectangle the scores will look like this:
| Your figure's name | rectangle |
| Reflection from top to bottom | Yes |
| Reflection from left to right | Yes |
| Reflection from left bottom to right top | No |
| Reflection from left top to right bottom | No |
| Rotation by 90 degrees | No |
| Rotation by 180 degrees | Yes |
| Rotation by 270 degrees | No |
| Symmetry Rank | 3 |
For a FourEars figure the scores will look like this:
| Your figure's name | FourEars |
| Reflection from top to bottom | No |
| Reflection from left to right | No |
| Reflection from left bottom to right top | Yes |
| Reflection from left top to right bottom | Yes |
| Rotation by 90 degrees | No |
| Rotation by 180 degrees | Yes |
| Rotation by 270 degrees | No |
| Symmetry Rank | 3 |
For a Propeller figure the scores will look like this:
| Your figure's name | Propeller |
| Reflection from top to bottom | No |
| Reflection from left to right | No |
| Reflection from left bottom to right top | No |
| Reflection from left top to right bottom | No |
| Rotation by 90 degrees | Yes |
| Rotation by 180 degrees | Yes |
| Rotation by 270 degrees | Yes |
| Symmetry Rank | 3 |
