No convex polygon with 7 or more sides will tessellate.
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True
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
Yes, it is true.
No, it is not true that you cannot tessellate a six-sided polygon by itself. Hexagons are a type of polygon that can tessellate, which means they can be arranged in a repeating pattern to completely cover a plane without any gaps or overlaps.
Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.