# Beauty of Three Dimensional Polyhedra and Spatial Visualization

## Applets and Games

• Geometry Games - numerous games. Many on 3D visualization.

• Cyberchase Point of View Game - Draw the side views for each of four people.

• Cut-outs, Nets - This applet folds a 2D net into a 3D object. Click and drag to manipulate the object/net.

• Cube Nets - A net is a two-dimensional figure that can be folded into a three-dimensional object. Which of the nets below will form a cube?

• Platonic Solids - Investigate the five Platonic solids (tetrahedron, cube (hexahedron), octahedron, dodecahedron, and icosahedron). Rotate the shape. Shift-click the edges and the faces to color (and count them). Can you make V - E + F = 2? (vertices - edges + faces = two)

• Platonic Solid Duals - Investigate the solids and their duals. The dual of a solid is formed by taking the midpoint of each face and making these midpoints the vertices of the new (dual) solid. For the dual, faces become vertices and vertices correspond to faces.

• Lathe (creating 3D objects) applet - fun, get creative!
• Truncate, Expand, Snubify - This is amazing! From the five platonic solids, you can get many of the Archimedean solids using these three processes. Very interesting.

• Great Bridge Building Game - Build a cargo bridge.

• Shape Explorer - Click "Show Score" to keep track of your number correct and incorrect. A shape is given and you have to determine the area and perimeter. Get 4 out of 5 correct and raise your hand for a sticker. ("Adjust the maximum size" three-clicks-to-the-right of the minimum.)
• Area Explorer - Set the perimeter and then change the shape and see what areas you can get. All shapes made of unit squares.
• Transformations Game - Four levels of play (do Levels 1, 2, 3, and 4). Use translation, rotation, reflection, and dilation.
• 3D Tetris - game
• Cube'O' - game

## Pages

 Archimedean Solids - (mine) videos, links, and even a cool Prezi! Volume and Surface Area Webpage - (mine) Prisms, Pyramids, Cylinders, and Cones - and paying attention to the Pythagorean theorem for the right triangles! Vi Hart's Site - 3D with food, balloons, and more! Blog is amazing. Great Video on the Hexaflexagon George Hart - Lots of cool 3D stuff. George is Vi's father. Eric Weinstsein's World of Mathematics - search for any mathematics term! Platonic Solids - includes nets for the five Platonic solids which you can print out -- on cards stock, cut out, and glue together (you should put tabs on the net when you cut it out so you have something to glue--the tabs end up on the inside of the solid). The icosahedron (#257) at the right, with three golden rectangles is by Tilman who has a Geometry Daily site.

## Other

• Cool video of an amazing piece of 3D art: (see also):

## Shared Graphics

James R. Olsen, Ph.D. ~ Western Illinois University
updated: October 31, 2015 10:44 AM