What you’ll learn
Identify rotational symmetry.
Key idea
A full turn partitions into equal vertex steps; a symmetry must advance an integer number of those steps.
A symmetry permutes the whole set by integer vertex steps; regularity alone does not make ninety degrees smallest.
Worked example
Classify examples and non-examples for the concept 'Identify rotational symmetry'.
A regular 6-gon has 6 equally spaced vertices on a circle of radius 2, centered at O. Does a 90-degree turn about O map it onto itself? Classify with vertex evidence.
- Adjacent vertex spacing is 360/6=60 degrees.
- A 90-degree turn advances 3/2 vertex steps, which is not integral, so an image vertex is not in the original set. The smallest positive symmetry is one vertex step.
Answer: No — 90 degrees advances 3/2 nonintegral vertex steps, so a vertex image misses the set.
Quick Check
Classify examples and non-examples for the concept 'Identify rotational symmetry'.
A regular 11-gon has 11 equally spaced vertices on a circle of radius 2, centered at O. Does a 90-degree turn about O map it onto itself? Classify with vertex evidence.