Tessellation Exploration: The Basics

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Objective: Find a method to tessellates the plane with any triangle. Introduce regular and semi-regular tessellations.

Tessellations by Triangles and Quadrilaterals

  1. Convince yourself that the parallelogram below will tessellate the plane. Draw your tessellation on a separate piece of paper. It should cover 1/4 of your page.
    Parallelogram.png
  2. Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
  3. Draw an acute, an obtuse and a right triangle. Now convince yourself of the fact that two congruent copies of the same triangle fit together to form a parallelogram or a rectangle.
  4. Why does this imply that all triangles will tessellate the plane?

    Tessellations of the Plane by Regular Polygons

    A regular tessellation is a tessellation made of regular, congruent, convex polygons.


    A semi-regular tessellation is a tessellation made of regular polygons of two or more types so that the arrangement of polygons at each vertex is the same.


  5. What is the common name for a regular 3-gon?
  6. What is the common name for a regular 4-gon?