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Q: Does a regular pentagon tessellate a plane with no overlaps or gaps?

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No not normally

No.

No.

Triangle, square and hexagon

Equilateral triangle, square and regular hexagon.

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No because the angles are not factors of 360 degrees

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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.

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!

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Square.

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