Midpoints
Midpoints are exactly what they sound like--the middle point of
line segments. One way to divide a polygon using midpoints is
to join the midpoints of consecutive sides. The polygon that results
replaces the original polygon.
An example of the midpoint technique applied to two different
polygons
|
|
Now let us consider the midpoint technique when applied to entire
tessellations:
An example of the midpoint technique applied to the 4.8.8 regular
tessellation. Note that after the original shapes are removed,
"empty space" remains. The "empty space" can be seen as a new
type of shape.
|
|
Following is a non-animated example that uses the midpoint technique.
Study it carefully.
|
(1)
The original tessellation of non-regular pentagons
|
(2)
The midpoints of each pentagon joined and colored green
|
|
(3)
The original tessellation removed
|
(4)
The "empty" spaces consist of two shapes: a triangle and a diamond.
These two shapes are now colored blue and red respectively.
|
|
|
Here is another non-animated example that uses the midpoint technique:
|
(1)
The original 3.12.12 / 3.4.3.12 demiregular tessellation
|
(2)
The midpoints of each polygon joined and colored a shade of green
|
|
(3)
The original tessellation removed
|
(4)
The "empty" spaces consist of two shapes: a triangle and a trapezoid.
These two shapes are now colored different shades of green.
|
|
|
  
 You may proceed to the templates page to access many ready-made
tessellations on which you can practice the division techniques.
|
top of the page
|
