It seems like your question got cut off. If you're asking about the influences on the shape, arrangement, or properties of tessellations (which are patterns made of one or more shapes that fit together without any gaps or overlaps), there are several factors to consider.
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Basic Shape: The fundamental shape used (triangles, quadrilaterals, hexagons, etc.) greatly affects the tessellation.
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Angles: The interior angles of the shapes determine whether they can tessellate. For example, shapes with angles that can sum up to 360 degrees when combined will tessellate effectively.
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Symmetry: The symmetry of the shapes can influence the aesthetic and functional properties of the tessellation.
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Rotation and Reflection: The ability to rotate or reflect shapes can introduce variety in the tessellation pattern.
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Coloring and Design: The way shapes are colored or patterned can influence the visual effects of the tessellation.
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Mathematical Rules: Geometric rules and principles underpin the tessellation's creation.
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