Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

## Geometric Solids

Pre-K-2, 3-5, 6-8, 9-12
Standards:
Math Content:
Geometry

This tool allows you to learn about various geometric solids and their properties. You can manipulate and color each shape to explore the number of faces, edges, and vertices, and you can also use this tool to investigate the following question:

For any polyhedron, what is the relationship between the number of faces, vertices, and edges?

This interactive is optimized for your desktop and tablet.

### Selecting a Shape

• Use the drop down menu to choose from the possible solids: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron, or "My Own Net."
• Manipulate set shapes in the workspace. Click and drag the shape to move.

### Modes

• Solid/Net: Toggle between solid and net to see different views of the selected shape.
• Color Palette: Select a color to color in faces, edges, and vertices. Click on elements to color them. Clicking again restores the default colors. As elements are colored, they are counted in the left panel. Note: In Net view, edges and vertices that overlap in Solid view only count once and are colored simultaneously.
• Zoom level: Zoom in and out by sliding the marker.
• Transparent: Makes all faces transparent, so the opposite side of solid is visible. Note: This view only disables coloring. When toggled off, previous coloring will be reinstated.
• Show Total: Will show use how many total faces, edges, and vertices there are.
• Print: Prints nets directly to the printer.
• Reset: Restores default coloring and orientation of shapes.

### Using "My Own Net"

Create your own net, and then print, cut, and fold to see if it forms a solid.

Select: Adds faces from the bank on the left and moves pieces.

Eraser: Erases individual faces.

Scissors: Cuts pieces at edges.

Color Palette: Colors faces, edges, and vertices as in other Select a Shape selections.

Note: When printing, note that all faces must be connected to create a single net.

Record the number of faces (f), edges (e), and vertices (v) for each shape. What relationship exists between f, e, and v? You can download and print the Exploring Geometric Solids Activity Sheet to guide your investigation.