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Using Polypad: Geometry

Introduction

This task provides an overview of using 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 ruler and protractor
  • Working with Penrose Tiles, Tantrix Tiles, Fractals, and Kolam Tiles
  • Geometric Constructions

Polygons

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 - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/y2QwRewKk7PheQ

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 Tool

Select a tool and click "Flip" to reverse the direction of the numbers on the tool.

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 - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/nil7UOvCf6a6BQ
Nature Tiles - Polypad - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/mrG9d6o7tWWV4g
Tantrix tiles - Polypad - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/3gtJ3mgPaJgBpA
Fractal - Polypad - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/TGC9JjZZ2AptQ
Kolam Tiles - Polypad - Mathigon
Virtual Manipulatives for Mathematics Classrooms: polygons, number and algebra tiles, fraction bars, tangram, pentominoes, and more.
https://mathigon.org/polypad/L58BIiF3RDywZw

Geometric Construction

Create a line or a polygon and then click on the three dots to see it's attributes.

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.

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