Making Math Visible

Wood Dome




Time Required: 1.5 Hours

Materials:
Notes:

1. The paper dome workshop is a great introduction to this activity and should be done first as it provides all the necessary background.
2. The template file is designed to make a dome two meters in diameter.  The parts can be scaled for other sizes, but all parts must be scaled the same amount.
3. Wood struts can be cut with a band saw or laser-cutter.  The laser-cutter file includes a hole for the cable ties to pass through.  If using a band saw, drill the holes.  You may need to sand the pieces to prevent splinters/slivers.
4. Only 6 five-slot hubs, 10 six-slot hubs, and 10 four-slot hubs are required for the final structure, but you will need the extras during assembly and in case of breakage.
5. The biggest challenge will be to keep track of the two different lengths of struts, as they are similar. You may want to make the difference clearer by using a wood stain (or marker) to color code the two lengths, as in the image above.
6. Eight-inch cable ties work well with struts made using the given file.  If you scale the file, you may need to use a different size cable tie. 
7. Zometool is an ideal manipulative for illustrating the structure of domes.  It has exactly the lengths and angles required for this particular structure.  If you don't have Zometool, you can improvise with other strut-and-node systems, such as straws and pipe cleaners, or toothpicks and marshmallows.
8. Students can work in groups to construct the modules.

Part A. Minds-On



1. Hand out blue and yellow Zometool struts and a supply of connector balls.  Giving as little instruction as possible, refer back to the paper dome and ask students to make a structure that is isomorphic to it using the Zometool materials.  They will discover that the yellow struts are slightly shorter than the blue struts and will conclude that the yellows should meet five at a vertex, with a blue pentagon surrounding. 

2. Discuss and review the structure and geometric properties of the dome.  In the image above, the yellow struts correspond to the edges of the underlying icosahedron.  The blue struts correspond to the colored lines that were drawn to create half-size triangles.



3. Point out that one can remove a "starfish" of five yellow struts to create a doorway if desired, as shown above.


Part B. Hands-On

1.  Give students a quick safety briefing about how to use cable ties. Cable ties should only be used for construction and can be dangerous if placed around any part of the body.



2. Students can work in either three or six groups as there are six modules to be assembled.  Divide the class up and hand out the wooden pieces accordingly.  There are two lengths of strut and three types of connector. A five-slot hub goes at the center of each pentagonal module.  The four-slot hub is a cut-off version of the six-slot hub, designed to sit comfortably with its flat edge on the floor.  The "ceiling module" will be slightly different from the five "floor modules" because it does not need four-slot hubs.



3. Ask students to make a pentagonal module using ten struts and six hubs.  Five short struts (green in the image above) come together to make a "starfish" with a five-slot hub (white in the image above) at the center.  This can be secured with a cable tie that makes a loop through the five holes.

4. Five long struts (blue in the image above) are added to make a surrounding pentagon.  In five of the modules, one of the long struts forms part of the base of the dome and needs to be connected with two four-slot hubs in order to rest comfortably on the ground. Cable ties can be added loosely, but not closed yet, as additional struts will need to be added later.

5. Before joining the modules together, ask students to visualize the entire dome by holding one module horizontally as the top center piece, and placing the other five around it, each with one strut on the floor.  They will see how the five remaining long struts fill in the base to make a circle.  They will also understand that when modules connect, one of the redundant hubs needs to be removed.



6. Ask students to work together, with some holding the modules in position while others make the connections.  First build the five sides of the dome, then add the ceiling.



8. If an opening is desired, remove a "starfish" of five short struts.



9.   Cut off the cable-tie tails and enjoy!



Part C. Conclusion

Ask students to compare this wood dome with the paper dome and their marked icosahedron to observe the analogous structures.  (This provides another example of an isomorphism, as introduced in the 12-Card Star workshop.)


Possible Extensions

See the Paper Dome Workshop Extensions.