WHY some shapes TESSELLATE while

others do not?

TESSELLATION[Regular]

Polygon Sides Angle Sum Interior AngleTriangle 3 180 60

Triangle

Does it tessellate?

But….. WHY?

How about the other polygons?

Polygon Sides Angle Sum Interior Angle

Quadrilateral 4 360 90

Pentagon 5 540 108

Hexagon 6 720 120

Octagon 8 1080 135

HOWEVER…!

Polygon Interior Angle

Pentagon 108

108+108+108 = 324108+108+108+108 = 432

The interior angles do not add up to 360o, therefore it means that regular pentagons do not tessellate.

Polygon Interior Angle

Octagon 135

135+135 = 270135+135+135 = 405

The interior angles do not add up to 360o, therefore it means that regular octagons do not tessellate.

They DON’T tessellate

THEREFORE,Tessellation must tile a floor with no overlapping or gaps, and they should be regular polygons.

To tessellate using the regular polygons, you need to use the ones that their interior angles add up to 360 degrees.

For triangles: interior angle = 60 degrees60+60+60+60+60+60 = 360

For squares: interior angle = 90 degrees90+90+90+90 = 360

For hexagons: interior angle = 120 degrees120+120+120 = 360

For pentagons: interior angle = 108 degrees108+108+108 = 324

More Examples!!![semi-regular]

6-3-6-3 TESSELLATION

Triangle’s interior angle: 60o

Hexagon’s interior angle: 120o

60o+120o+60o+120o

= 180o+180o = 360o

8-8-4 Tessellation

&Interior

angle of an octagon:

135O

Interior angle of a

square: 90O

135o+90o+135o

= 360o

12-4-6 Tessellation

Interior angle of a

square: 90O

Interior angle of a hexagon:

120O

Interior angle of a

dodecagon: 150O

150o+120o+90o

= 270o+90o

= 360o

CONCLUSION

If you want to tessellate regular shapes, you need to

use the ones that their interior angles add up to

360 degrees.

By ELLY LEE