B3D

Beauty of Three Dimensional Polyhedra and Spatial Visualization

• 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.

• Truncate, Expand, Snubify - From the five platonic solids, you can get other solids using these three processes. The main thing we will look at is truncate.

• 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

under construction

• 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).

• Wofram Demonstrations Project - Lots a really neat dynamic representations of mathematical ideas, including three-dimensional objects. One example is the Octahedron Fractal.
• Poly - a shareware program for exploring and constructing polyhedra. Manipulate solids and their nets. Fold and unfold nets. Pedagoguery Software Inc. in Canada

James R. Olsen, Ph.D. ~ Western Illinois University
updated: March 28, 2009 12:37 PM