Polygons

Updated August 21, 2026 20:28

Use polygons to create dynamic shapes in the Desmos Graphing Calculator, Geometry Tool, and 3D Calculator.

Watch the video for an introduction to polygons in Desmos, and read on to learn more.

Polygon Function

$Graph showing \operatorname{polygon}\left((-2,2),(2,2),(0,-2)\right). Then using the polygon function and plotting points in the graph paper to create a polygon. GIF$

In the Graphing Calculator and Geometry Tool, use the polygon function with coordinates that represent the vertices of a polygon.

$Graph showing a polygon with mobable vertices. Expression line 1: A=\left(-2,2\right). Expression line 2: B=\left(2,2\right). Expression line 3:C=\left(0,-2\right) . Expression line 4:\operatorname{polygon}\left(A,B,C\right) . Screenshot.$

Create a polygon with movable vertices by naming the coordinate points of each vertex of the polygon.

$Image of a polygon. Expression line 1: table with coordinates (-2,2),(2,2),(0,-2). Expression line 2: \operatorname{polygon}\left(x_{1},y_{1}\right). Screenshot.$

Or, create a polygon by creating a table containing the vertices of a polygon.

Polygon Tool in Geometry

Another way to create a polygon in the Geometry Tool is to use the Polygon tool .

Select Polygon from the toolbar and then click the graph paper to choose points as the vertices of the polygon. Be sure to click back to the starting point to close your polygon.

You can also double-click on the last vertex of your polygon to close it automatically.

Using the Geometry toolbar polygon function to plot points and create a polygon and triangle. GIF.

Create a Triangle in 3D

The 3D Calculator does not support the polygon function. However, you can use the triangle function along with three points to create a triangular surface.

Transformations of Polygons

Transform polygons from the expression list or with the Transformation tool in Geometry.

In this example, the polygon is transformed using the expression list in the Graphing Calculator. It’s dilated by a factor of $2$, and translated $6$ units horizontally and $-8$ units vertically.

$Image of a polygon and a transformation of the polygon. Expression line 1: table with coordinates (-2,2),(2,2),(0,-2). Expression line 2: \operatorname{polygon}\left(x_{1},y_{1}\right). Expression line 3: \operatorname{polygon}\left(2\left(x_{1}+3\right),2\left(y_{1}-4\right)\right). Screenshot.$

In the Geometry Tool, you can find the Transformation tools in the toolbar after you select a polygon.

To learn more about transformations in the Geometry Tool, visit Transformations: Desmos Geometry.

Polygon Options Menu

Click and hold the Color icon to open a polygon's Options menu. From there, you can show or hide the outline of the polygon, change the outline opacity and width, toggle the fill on or off, and adjust the fill opacity.

Image of the polygon option menu. Screenshot.

Learn More

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