Section 14-5
Math 366 Lecture Notes
Section 14.5 – Tessellations of the Plane
A tessellation of a plane (or space) is the filling of the plane (or space) with repetitions of figures
in such a way that no figures overlap and there are no gaps.
John Locke
M.C. Escher
A regular tessellation is a tessellation made up of one type of regular polygon.
Which regular polygons tessellate the plane?
If a regular polygon tessellates the plane, the sum of the congruent angles of the polygons around
every vertex must be 360°.
Semiregular Tessellations
When more than one type of regular polygon is used and the arrangement of the polygons at each
vertex is the same the tessellation is semiregular.
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Section 14-5
Tessellating with Other Shapes
Successive half-turns of a quadrilateral about the midpoints of the sides will produce four
congruent quadrilaterals around a common vertex, and the figure will tessellate the plane.
Other types of polygons can tessellate the plane.
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