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Not all shapes can tessellate. For example a pentagon will not tessellate.

Only those shapes where the angles of the vertices which meet sum to 360° (a full turn) will tessellate.

For example, with a regular hexagon, each angle is 120° and when three come together they form 3×120° = 360° and so will tessellate, but with an octagon, each angle is 135°; two such angles form 2×135° = 270°, but three such angles form 3×135° = 405° - two octagons will lay together with a gap, but three octagons will overlap: they cannot tessellate; however, 360° - 270° = 90° which is the angle of a square, so octagons together with squares will tessellate.

Q: Why can any shape tessellate?

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Any shape tesselates any of its covering spaces.

transversal

Yes. Any shape can tessellate if you allow other shapes. The simplest way is to select the other shapes so that the given shape and the "other shapes" can be combined to make a rectangle or square.

Some 3D shapes will tessellate as for example a brick wall

Yes because all 4 sided quadrilaterals will tessellate

Related questions

Any shape tesselates any of its covering spaces.

A regular pentagon will not tessellate.

No.

Yes, any quadrilateral will tessellate.

There are many shapes: circles, ellipses, ovals (elongated circles), cardioids, any shape with a "hole" in it such as a annulus.Polygons will tessellate if combined with other suitable polygons.

Yes

No

transversal

Some 3D shapes will tessellate as for example a brick wall

Yes. Any shape can tessellate if you allow other shapes. The simplest way is to select the other shapes so that the given shape and the "other shapes" can be combined to make a rectangle or square.

Yes because all 4 sided quadrilaterals will tessellate

Yes. For example, any triangle, including a scalene triangle, will tessellate.