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# How many regular polygons will tessellate in the euclidean plane?

Updated: 11/19/2022

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Q: How many regular polygons will tessellate in the euclidean plane?
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### What does semi regular tessellation have?

It has two regular polygons which can be used together to tessellate a plane.

### What regular polygons can tessellate a plane with no overlaps or gaps?

Triangle, square and hexagon

### Which regular polygons can tessellate a plane with no overlaps or gaps?

Equilateral triangle, square and regular hexagon.

### How many regular polygons does it take to tessellate a graph plane?

The answer depends on the size of the plane and of each polygon.

### Which ragular polygons can tessellate a plane with no overlaps or gaps?

Equilateral triangle, square and regular hexagon.

### Which polygon will not tessellate a plane?

Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation.

### Which polygons will tile the plane?

If it's interior angle is a factor of 360 then it will tessellate such as a square, a regular hexagon and an equilateral triangle.

### Can heptagon tessellate?

No. Equilateral heptagons (7 sided figures) do not tessellate the plane. Not if no other polygons are allowed. But if you allow a (non-equilateral) pentagon then you might be able to tessellate the plane!

### What types of figures tessellations the plane?

All sorts of figures. The only regular polygons that can tessellate by themselves are triangles, squares and hexagons. Irregular polygons such as rectangles, rhombuses, parallelograms and trapeziums will as well. Regular octagons combined with squares will. Other regular polygons can be combined with appropriate star-shapes to tesselate. There are also Penrose tilings which, although they cover the plane, are non-periodic in the sense that the pattern does not repeat itself if you move along. Finally there are many irregular shapes that will tessellate.

No

Square.

No.