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You cannot tessellate seven-sided polygons by themselves?
The heptagon (7 sided polygon) cannot tessellate. The exterior angle of the heptagon is 51.43 degrees which makes the interior angle 128.57 degrees.
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.
