# Difference between revisions of "Tessellation Exploration: The Basics"

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<li> Why does this imply that all triangles will tessellate the plane? | <li> Why does this imply that all triangles will tessellate the plane? | ||

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==Tessellations of the Plane by Regular Polygons== | ==Tessellations of the Plane by Regular Polygons== | ||

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A {{define|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. | A {{define|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. | ||

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<li> What is the common name for a regular 3-gon? | <li> What is the common name for a regular 3-gon? | ||

<li> What is the common name for a regular 4-gon? | <li> What is the common name for a regular 4-gon? |

## Revision as of 12:36, 18 May 2007

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

## Tessellations by Triangles and Quadrilaterals

- 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.
- Show that a square tessellates the plane and show that a rectangle tessellates the plane. Your tessellations should cover 1/4 of your page.
- 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.
- 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.

<ol|start=4>