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You cannot tessellate eight-sided polygons by themselves?
True
Is there such thing as a 3D hexagon?
No. Regular hexagons tessellate and cannot form a 3-d shape.No. Regular hexagons tessellate and cannot form a 3-d shape.No. Regular hexagons tessellate and cannot form a 3-d shape.No. Regular hexagons tessellate and cannot form a 3-d shape.
Explain why regular polygons with more than 6 sides will not tessellate?
The tessellating polygons must meet at a point. At that point, the sum of the interior angles of the polygons must 360 degrees - the sum of angles around any point. Therefore, each interior angle must divide 360 evenly. The interior angles of regular polygons with 7 or more sides lie in the range (120, 180) degrees and so cannot divide 360.
Why can't a regular octagon tessellate?
To be able to tessellate where a vertex meets other vertices, the total of those angles must be a full circle of 360°. The interior angle of an Octagon is 135° which does not divide into 360° which means there cannot be a complete number of vertices meeting and so it cannot, by itself, tessellate. However, two octagons meeting at a point would have 135° + 135° = 270° leaving 90° which is the interior angle of a square. So octagons and squares together will tessellate.
Why can't circles tessellate?
For a shape to tile a plane, it must be capable of sharing a border with a copy of itself. Circles cannot do this; two circles which do not overlap touch in at most one point.
