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Regular shapes are both equilateral and equiangular. Irregular shapes may or may not be equilateral and equiangular.
Each body has its own centre of gravity. The centre of gravity of two regular shapes - an equilateral triangle and a square will be different so why should the cog of a regular and an irregular shape not be different?
Irregular shapes are all around. Most shapes are irregular.
an circle and shapes that are not regular dumhead
A regular and an irregular octagon both have 8 interior angles