Why are tesserae used in mosaic art cut into regular shapes?

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In mosaic art, tesserae are cut into regular shapes, such as squares or triangles, primarily to allow them to fit closely together within the grid that forms the mosaic surface.1

This technique was developed by the Greeks as an evolution from using uncut, natural pebbles. The motivation behind creating these uniform, geometric pieces was to achieve a densely set, refined image that could rival the quality and splendor of contemporary paintings. By using regular shapes, artists could create a cohesive, tightly packed surface, which was particularly essential for floor mosaics where durability and resistance to wear were primary requirements.1