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.
Hansen, Joel; Marquez, Itzamar; Roychowdhury, Mrinal Kanti; and Torres, Eduardo, "Quantization coefficients for uniform distributions on the boundaries of regular polygons" (2020). Mathematical and Statistical Sciences Faculty Publications and Presentations. 72.