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Q: Do all shapes tessellate

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I believe that regular shapes will only tessellate if the sum of their internal angles is a multiple of 180.

Yes it does tessellate. * * * * * That is simply not true. No polygon with 7 or more sides will tessellate with identical shapes.

If their shapes are suitably matched they can tessellate together.

Shapes tessellate to fit around an interior angle. They also tessellate because they are regular polygons; non-regular polygons cannot tessellate. * * * * * Not correct. All triangles and quadrilaterals will tessellate, whether regular or irregular. Contrary to the above answer, a regular pentagon will not tessellate but there are 14 different irregular pentagons which will tessellate (the last was discovered in 2015). Three convex hexagons will do so as well. No polygon of 7 or more sides will tessellate - whether they are regular (contrary to the above answer) or irregular.

In geometry, when quadrilaterals tessellate, they fill a finite or infinite space with no overlaps or gaps between shapes. All quadrilaterals tessellate because they can all be linked together side by side in some shape or form with no overlaps. In geometry, when quadrilaterals tessellate, they fill a finite or infinite space with no overlaps or gaps between shapes. All quadrilaterals tessellate because they can all be linked together side by side in some shape or form with no overlaps.

Related questions

For any polygon, there will be other shapes such that, together, they can tessellate.

All regular polygons whose interior angles are a factor of 360 degrees will tessellate with themselves

yes, most regular shapes can tessellate :)

I believe that regular shapes will only tessellate if the sum of their internal angles is a multiple of 180.

yess

Yes it does tessellate. * * * * * That is simply not true. No polygon with 7 or more sides will tessellate with identical shapes.

Yes all 4 sided quadrilaterals will tessellate

If their shapes are suitably matched they can tessellate together.

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

Triangles.

Quadrilaterals (4 sides) will tessellate because thier interior angles add up to 360 degrees.

Shapes tessellate to fit around an interior angle. They also tessellate because they are regular polygons; non-regular polygons cannot tessellate. * * * * * Not correct. All triangles and quadrilaterals will tessellate, whether regular or irregular. Contrary to the above answer, a regular pentagon will not tessellate but there are 14 different irregular pentagons which will tessellate (the last was discovered in 2015). Three convex hexagons will do so as well. No polygon of 7 or more sides will tessellate - whether they are regular (contrary to the above answer) or irregular.

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