http://www.ck12.org Chapter 12. Rigid Transformations
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
- How many regular hexagons will fit around one point?
- Does a regular octagon tessellate?
- 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:
- 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. - 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◦.
Explore More
Will the given shapes tessellate? If so, how many do you need to fit around a single point?
- A regular heptagon
- A rectangle
- A rhombus
- A parallelogram
- A trapezoid
- A kite
- A regular nonagon
- A regular decagon
- A completely irregular quadrilateral
- In general, which regular polygons will tessellate?
- Use equilateral triangles and regular hexagons to draw a tessellation.
- The blue shapes are regular octagons. Determine what type of polygon the white shapes are. Be as specific as
you can.