7. Group Actions or Advanced Group Topics
Symmetry Applications — Quiz
Test your understanding of symmetry applications with 5 practice questions.
Practice Questions
Question 1
How many rotational symmetries does a regular square have?
Question 2
In the full symmetry group of a square, what is the size of the orbit of one vertex?
Question 3
In the full symmetry group of a square, what is the size of the stabilizer of a fixed vertex?
Question 4
Which theorem is commonly used to count distinct colorings up to symmetry?
Question 5
A square's vertices are colored with exactly $1$ black vertex and $3$ white vertices. How many distinct colorings are there up to symmetry?