Poly allows the user to view and interact with polyhedra and their nets, thus connecting two and three dimensional geometries.
Exploring The Software:
- Begin by going to the File menu and opening "Preferences". I suggest you check "3-D Shaded", "3-D Edges", and "2-D Net" views.
- Start with one of the Platonic Solids. Select the 3-D shaded view. To explore one of the interactive options, try a demonstration routine under View > "Start Demo". You can control this action with a click-&-drag on the slider, or have the slider move automatically with a grab-drag-&-release action.
- Another interactive option is to grab-&-drag the figure in the viewing field, or use a grab-drag-&-release action to put it into motion.
- You can use the View > "Printer" to set up what you'd want to have printed on a handout.
- You can get information about the polyhedra categories in the Help menu.
Thinking About the Mathematics:
- A net is an arrangement of connected polygons that become faces when the two dimensional net is folded to form a three dimensional solid. Note the arrangement of the squares in the net shown for the cube. How many other nets could be folded into a cube? How many arrangements of four triangles can be folded into a tetrahedron? Based on thinking about these two examples how many possible nets do you expect to find for the octagon? For which of the Platonic and Archimedian solids can you have symmetrical nets?
- You would want to add tabs to a printed net in order to create a polyhedron. Where would the best places be to add tabs for a given figure?
- Each of the Platonic and Archemedian solids exhibits 2-fold and 3-fold symmetries, and is said to belong to either the "2-3-4" or "2-3-5" symmetry family depending on whether it also exhibits 4-fold or 5-fold symmetry. That is, the solid exhibits 2-fold, 3-fold, 4-fold and/or 5-fold symmetries centered about a vertex, edge, or face. Rotating the closed figures helps visualize these different symmetries.
- What is the essential characteristic that determines whether a solid is in the 2-3-4 or 2-4-5 family?
- How many polyhedra can you identify that exhibit only one symmetry? How many polyhedra can you find that exhibit two symmetries? What combinations are possible or not possible?