Illuminations: Tessellation Creator

# Tessellation Creator

A tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. What kind of tessellations can you make out of regular polygons?

### Instructions

 Click-and-drag the shapes from the top menu to the canvas below. If the sides of shapes are dragged close to each other, those shapes will snap together. Click-and-drag a rectangle around a group of shapes to glue them together. Use the scroll bars along the right side and bottom of the canvas to view different parts of the canvas. The buttons along the left side can be turned on to use their functionality, which is described below. Each of these buttons can be turned off by clicking anywhere on the canvas. Eraser – Click on any shape, and it will be removed from the canvas. Rotate – Click on any shape, and it will be rotated 10° clockwise. Zoom In/Zoom Out – These buttons will zoom in or out on the entire canvas. All shapes, including new ones after you click zoom in/zoom out, will be resized appropriately. Copy – Click this button to copy the last shape selected. To copy all shapes, first click-and-drag a rectangle around the shapes to glue them together. Hammer – Click on any group of glued shapes, and it will break it apart into the original polygons. Paint – Select a color, and then click on a shape to change its color. Clear – This is a dangerous button! Pressing it will remove all objects from the canvas.

### Exploration

 What shapes tessellate? If shapes can be combined to make patterns that repeat and cover the plane, then they tessellate. What patterns can you find? Which of the shapes tessellate by themselves? Can you cover the plane with just triangles? just squares? just pentagons? Try to find a way to make a tessellation with just squares and octagons. Which other combinations of shapes tessellate? Is there a way to tell if shapes with tessellate by looking at the properties of those shapes? How? Hint: The length of the sides of all the shapes are all the same. Only the angles are different. What are the angles in each shape?

### Lessons

 More and Better Mathematics for All Students
 © 2000 National Council of Teachers of Mathematics Use of this Web site constitutes acceptance of the Terms of Use The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.