CK-12 Geometry Concepts

http://www.ck12.org Chapter 12. Rigid Transformations

This is the final tessellation. You can continue to tessellate this shape forever.

Now, continue to fill in around the figures with either the original or the rotation.

Example B

Does a regular pentagon tessellate?

First, recall that there are( 5 − 2 ) 180 ◦= 540 ◦in a pentagon and each angle is 540◦÷ 5 = 108 ◦. From this, we know
that a regular pentagon will not tessellate by itself because 108◦× 3 = 324 ◦and 108◦× 4 = 432 ◦.

Example C

How many squares will fit around one point?

First, recall how many degrees are in a circle, and then figure out how many degrees are in each angle of a square.
There are 360◦in a circle and 90◦in each interior angle of a square, so^36090 =4 squares will fit around one point.

Watch this video for help with the Examples above.

MEDIA

Click image to the left for more content.

CK-12 Foundation: Chapter12TessallationsB

Concept Problem Revisited

You could tessellate a regular hexagon over a plane with no overlaps or gaps because each of its interior angles is
120 ◦. Three hexagons whose angles sum to 360◦surround each point in the tessellation.

Vocabulary

Atessellationis a tiling over a plane with one or more figures such that the figures fill the plane with no overlaps
and no gaps.

Guided Practice

1. How many regular hexagons will fit around one point?


2. Does a regular octagon tessellate?


3. Tessellations can also be much more complicated. Check out http://www.mathsisfun.com/geometry/tessellation.
   html to see other tessellations and play with the Tessellation Artist, which has a link at the bottom of the page.

Answers:

1. First, recall how many degrees are in a circle, and then figure out how many degrees are in each angle of a regular
   hexagon. There are 360◦in a circle and 120◦in each interior angle of a hexagon, so^360120 =3 hexagons will fit around
   one point.


2. First, recall that there are 1080◦in a pentagon. Each angle in a regular pentagon is 1080◦÷ 8 = 135 ◦. From this,
   we know that a regular octagon will not tessellate by itself because 135◦does not go evenly into 360◦.