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

Updated: 10/17/2022

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12y ago

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yes

no yes no

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12y ago
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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.

### 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.

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

Equilateral triangle, square and regular hexagon.

### Do Congruent regular pentagon's tessellate a plane?

No because the angles are not factors of 360 degrees

yes

### Can a tesellation be created with any shape you can think of?

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.

### Describe a combination of a regular octagon and another regular polygon that will tessellate the plane?

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

### 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!

### Is a rectangle tessellate?

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