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Q: Is the quadrilateral tessellation a regular tessellation?

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A "tessellation" (also called a "tiling") of a plane region is a covering of that 2-dimensional region using shapes that don't overlap and don't leave any gaps uncovered. Typically, we are interested in trying to use shapes that are congruent (all the same size and shape) regular polygons (the angles and sides of each polygon are the same), such as an equilateral triangle, a square, a regular pentagon, etc. This is called a "regular tessellation". It has been shown that the only regular polygons that tessellate are equilateral triangles, squares, and hexagons. So for example, a regular pentagon can't be used to tile a floor, because the angles don't match up as needed and will leave gaps on the floor that would need a different shape to fill them in. Consider, for example, a regular octagon. Each interior angle is 135o. So if you put two octagons next to each other, sharing a common side, then the two interior angles would combine to be 270o. But that leaves only another 90o of the full 360o at the point the two edges meet and need another shape to complete the tiling, which is not enough room to squeeze in another octagon that would take up 135o. The 90o does allow enough room for a square, however, and in fact octagons and squares can be combined to tile a floor in what is called a "semiregular tessellation" (using more than one shape).

tessellations are designs that are based on a shape that regularly tiles smoothly, such as squares or hexagons. Geometrically, this guarantees that all the space is accounted for, and that the shapes should fit together ( though not necessarily smoothly). If you take a square or hexagon (or any other regular shape that fits together by itself) and cut out parts of it using scissors, then attach the cut out parts on the opposite edge of the square from which they were removed, you should end up with a working tessellation.

It will tessellate if its vertices divide into 360 degrees evenly. The only regular polygons that will tessellate are an equilateral triangle, a square and a regular hexagon. There are other, non-regular, polygons that will tessellate.

A door, window, photograph, book, floor,,computer, trak pad, computer screen

"yes"The answer above is incorrect. it was proven hundreds of years ago that regular pentagons do NOT tessellate. there are methods for tessellating pentagons, but they are not regularpentagons.yes the answer in the middle is write polygons can not tessellate

Related questions

No, it is not because a quadrilateral is generally not a regular polygon.

Tessellation is defined as the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions. A periodic tiling has a repeat pattern. A regular quadrilateral can be used by itself to make a tessellation.

A regular triangle, quadrilateral (i.e., square) and hexagon may be used.

A regular tessellation or semi-regular tessellation or none.

Yes, any quadrilateral can be used.

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It is a regular tessellation.

A regular tessellation is based on only one regular polygonal shape. A semi-regular tessellation is based on two or more regular polygons.

A regular tessellation uses only one regular polygon. A semi-regular tessellation is based on two or more regular polygons.

There is no such thing as a seni-regular tessellation. A semi-regular tessllation is a tessellation using two regular polygons: for example, octagons and squares together.

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