Illuminations: Geometric Solids

# Geometric Solids

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?

### Instructions

 Select a Shape: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron Manipulate set shapes in the workspace. Click and drag the shape to move. 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. 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. Shaded: Add shading to faces to make solids appear more three-dimensional. Zoom level: Zoom in and out by sliding the marker. Print: Prints nets directly to the printer. Reset: Restores default coloring and orientation of shapes.   Select a Shape: 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. Zoom level: Zoom in and out by sliding the marker. Print: Prints nets directly to the printer. Note: All faces must be connected to create a single net. Reset: Clears the workspace.

### Exploration

 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.

### Lessons

 More and Better Mathematics for All Students
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