12.7. Tessellations http://www.ck12.org
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 use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52458CK-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.