Yes
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A chessboard is tessellated, so I assume it is a figure that is checkered.
A plane can be tessellated by triangles, various quadrilaterals, 15 types of convex pentagons (latest discovered in 2015) and various hexagons. No convex polynomial with 7 or more sides will tessellate.
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no it can not i have research it thoroughly i could not find any pictures of a regular decagon tessellated. i did but they all had different shapes so the answer is no it is not logically possible
Yes. A simple case would be where they combine into a square.