Quantization coefficients for uniform distributions on the boundaries of regular polygons

In this paper, we give a general formula to determine the quantization coefficients for uniform distributions defined on the boundaries of different regular \(m\)-sided polygons inscribed in a circle. The result shows that the quantization coefficient for the uniform distribution on the boundary of a regular \(m\)-sided polygon inscribed in a circle is an increasing function of \(m\), and approaches to the quantization coefficient for the uniform distribution on the circle as \(m\) tends to infinity.