House of Math

How to Make a Polyhedron in GeoGebra

You can use GeoGebra to draw polyhedra, such as a tetrahedron, octahedron, cube, or dodecahedron. It can also display the total volume of the polyhedron you create.

GeoGebra Instruction 1

Drawing a Tetrahedron

1.: Open Algebra View and Graphics View under View in Menu.
2.: Select the tool Regular polygon , which is the fifth item in the Toolbar and the second tool from that list.
3.: Draw an equilateral triangle by clicking on two points in Graphics View. These will be two of the vertices of the triangle. When GeoGebra asks you how many vertices you want, type 3.
4.: Close Graphics View and open 3D Graphics under View in Menu.
5.: Click on an empty space in 3D Graphics to update Toolbar with new tools. Select the tool Tetrahedron from the ninth item in the Toolbar (Pyramid ) and the seventh tool from that list.
6.: Click on the triangle you made in Step 4.

The tetrahedron will now appear in 3D Graphics. The volume of the tetrahedron will appear in Algebra View.

GeoGebra Instruction 2

Drawing an Octahedron

1.

Open Algebra View and Graphics View under

View in

Menu.

2.

Select the tool Regular polygon

, which is the fifth item in the Toolbar and the second tool from that list.

3.

Draw an equilateral triangle by clicking on two points in Graphics View. This will be two of the vertices of the triangle. When GeoGebra asks you how many vertices you want, type 3. Pay attention to the name of the triangle, since it will be used in a later step. GeoGebra will call it poly1 if it’s the first figure you’ve created in this session.

4.

Close Graphics View and open 3D Graphics under

View in

Menu.

5.

In a new row in Algebra View, type in

Octahedron

and select

Octahedron(<Equilateral Triangle>)

among the options that appear. Replace <Equilateral Triangle> with the name of your triangle from Step 3.

The octahedron will now appear in 3D Graphics. The volume of the octahedron will appear in Algebra View.

GeoGebra Instruction 3

Drawing an Icosahedron

1.

Follow Steps 1–4 in Item 5.

2.

In a new row in Algebra View, type in

Icosahedron

and select

Icosahedron(<Equilateral Triangle>)

among the options that appear. Replace <Equilateral Triangle> with the name of your triangle from Step 3 in Item 5.

The icosahedron will now appear in 3D Graphics. The volume of the icosahedron will appear in Algebra View.

GeoGebra Instruction 4

Drawing a Cube

1.: Open Algebra View and Graphics View under View in Menu.
2.: Select the tool Regular polygon , which is the fifth item in the Toolbar and the second tool from that list.
3.: Draw a square by clicking on two points in Graphics View. These will be two of the vertices of the square. When GeoGebra asks you how many vertices you want, type 4.
4.: Close Graphics View and open 3D Graphics under View in Menu.
5.: Click on an empty space in 3D Graphics to update Toolbar with new tools. Select the Cube tool from the ninth item in the Toolbar (Pyramid ) and the eighth tool from that list.
6.: Click on the square you made in Step 3.

The cube will now appear in 3D Graphics. The volume of the cube will appear in Algebra View.

GeoGebra Instruction 5

Drawing a Dodecahedron

1.

Open Algebra View and Graphics View under

View in

Menu.

2.

Select the tool Regular polygon

, which is the fifth item in the Toolbar and the second tool from that list.

3.

Draw a regular pentagon by clicking on two points in Graphics View. These will be two of the vertices of the pentagon. When GeoGebra asks you how many vertices you want, type 5. Pay attention to the name of the pentagon, since it will be used in a later step. GeoGebra will call it poly1 if it’s the first figure you’ve created in this session.

4.