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

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

No not normally

No.

Triangle, square and hexagon

Equilateral triangle, square and regular hexagon.

No because the angles are not factors of 360 degrees

Related questions

No not normally

No.

No.

Triangle, square and hexagon

Equilateral triangle, square and regular hexagon.

Equilateral triangle, square and regular hexagon.

No because the angles are not factors of 360 degrees

yes

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.

A regular octagon can tessellate the plane when combined with regular squares. By placing a square in the center of the octagon and surrounding it with eight octagons, the shapes can be repeated infinitely, filling the plane without gaps or overlaps

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!

The rectangle is the simplest and most obvious case of a geometrical form that can tile a plane.