12.2.2 Tessellations (continued)
A tessellation is classified as regular, semiregular, or neither in this example. This tessellation is semiregular because it consists of two kinds of regular polygons that meet in the same numbers at each vertex. The polygons are an equilateral triangle and a hexagon.
A tessellation is classified as regular, semiregular, or neither in this example. This tessellation is neither regular nor semiregular because it consists of polygons that are not regular (their angles are not all equal).
Example 4 Determining Whether Polygons will Tessellate
It is determined in this example whether a regular polygon can be used to form a tessellation and why. Physically, there does not appear to be a way to tessellate the regular octagons. To find the internal angles of a regular octagon, divide the octagon into three quadrilaterals, as shown, whose internal angles sum to 1080°. Dividing 1080° by the number of internal angles in the regular octagon, 8, gives 135° per angle. The angles around a vertex in the tessellation must sum to 360°, and 135° does not divide evenly into 360°, so it is clear why the figures will not fit together in a tessellation.
325
Made with FlippingBook - PDF hosting