All Lesson Plans

Using Polypad: Geometry


This tutorial provides an overview of the Geometry tiles. Below are the topics covered.

  • Working with Polygons - rotating, flipping, cutting, and more.
  • Creating custom polygons
  • Joining Polygons
  • Tessellations with Pentagons
  • 3D Solids
  • Using the Utensils
  • Working with Penrose Tiles, Tantrix Tiles, Fractals, and Kolam Tiles
  • Geometric Constructions


Rotations and Snapping Polygons

Flipping Polygons

Cutting Polygons

Custom Polygons

Use the custom polygon to create a polygon of any size with any number of vertices. Click on an edge to add a vertex and click on a vertex to remove it. The vertices snap to grid lines as well. Select "Fix Vertices" from the toolbar to prevent any more changes to the custom polygon.

Joining Polygons

Select multiple polygons and then click "Join" to create a combined Polygon.

Pentagon Tilings

Regular pentagons don’t tessellate, but there are 15 types of irregular pentagons that do – the last of which was only discovered in 2015. Here is one example.

Pentagon Tiling – Polypad

3D Solids

Use the polygons to construct a net of a 3D object. Not all creations will be a valid polyhedron net. Below are some examples using squares. Click here to see some other examples.

Click "Unfold" or use the slider to unfold the polyhedron back into a net. Once unfolded, click "Unfold" again to separate the net back into individual polygons.

Using the grid background with the custom polygon can be helpful in creating nets.


Ruler and Protractor

Change units on by clicking on the gear in the action bar. Click Flip to reverse the direction of the numbers on the ruler and protractor. Use the black circles to change the size of each tool.


Use the compass tool for a variety of geometric constructions. Visit the task page to explore lessons using geometric constructions.

Patterns and Art

Penrose Tiles, Kolam Tiles, Fractals, and Tantrix Tiles

See the Polypad's below for an examples of how these tiles can used to make all sorts of designs!

Penrose Tiling – Polypad
Nature Tiles – Polypad
Tantrix tiles – Polypad
Fractal – Polypad
Kolam Tiles – Polypad

Geometric Construction

Use the construction tools to create lines, circles, rectangles and more. Click on the gear icon to label various parts of a shape. $a = area, $l = length, $c = circumference, $p = perimeter, $d = degrees, and $r = radians. Watch this video to learn more.

When selecting a shape, a variety of construction options appear at the bottom of the canvas.

Use the "Invisible" option to hide parts of a construction.

Explore our Tasks and Learn More

Visit the Activities page to see lesson plans, student explorations, puzzles, and teaching ideas and visit the Tutorial page to learn more.