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Q: Can a regular pentagon tessellate without overlaps or gaps?

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No, there would be triangles in between. Sorry!

Equilateral triangle, square and regular hexagon.

No. Multiple copies of the shape - whether arranged side-by-side or in an interlocking pattern, must cover a plane area without gaps or overlaps. A circle or regular pentagon, for example, will not tessellate.

The angles of a regular pentagon are 108 degrees in measure. That angle can not duplicate and make 360 degrees so it will tessellate or cover 360 without gaps.

A regular tessellation is one in which a plane is covered, without gaps or overlaps, using copies of a regular polygon.

No a pentagon is a single polygonal shape, A tessellation is a scheme for covering a plane, without gaps of overlaps, using multiple copies of the same basic shape. These are usually polygons.

It is a regular tessellation.

A scheme for suing multiple copies of a regular polygon so as to cover a plane without gaps or overlaps.

A pentagon is a 2D, five sided shape. A regular pentagon looks a bit like a house, with a square without a top and instead a point.

A tessellation is created when a shape is repeated and covers a plane without any gaps or overlaps. All of a regular polygon's angles and sides are congruent. If we tessellate the Euclidean plane with a regular polygon, the tessellation is a regular tessellation. Only three regular polygons can tessellate the Euclidean plane: triangles, squares, or hexagons. Since the regular polygons in a tessellation must fill the plane at each vertex, the polygon's interior angle measure must be an exact divisor of 360 degrees. This only works for the triangle, square, and hexagon and is the reason why only they can tessellate the Euclidean plane. Some tessellations are made with figures of animals such as birds. M.C. Escher is famous for his work with tessellations including ones with animals. Some links are included to show more about tessellations.

No circles can't tessellate because tessellate means fits together without any gaps and overlaping. I hope this helps =]

Shapes can tessellate only if a number of them can meet at a point and cover 360 degrees without overlap. For regular shapes this requires that the angles of the shape are a factor of 360 degrees. For non-regular shapes it is necessary that the angles of the shapes can be grouped so that they sum to 360 degrees.

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