12 APPENDIX II: Model Making

12  APPENDIX II: Model Making

2Tensegrity Icosa (See drawing, page 236)

3 You need some %" dowel, a dozen little picture-framers’ screw eyes, wire no finer than #28. Cut six sticks, each 9" long; put a screw eye at each end. Cut twenty-four pieces of wire, each 10" long. With a pencil, number the two ends of the first stick, 1 and 2, the next 3 and 4, and so on on up to 11 and 12.

4 When you wire it up, each wire runs 5y₈"> screw eye to screw eye. Cut a strip of cardboard this length to measure with. Connect as follows, referring to your penciled numbers. When you finish, there will be four wires at every screw eye.

1.

to 11, 1 to 12; 3 to 11, 3 to 12. Let sticks 1-2 and 3-4 lie parallel, with stick 11-12 sandwiched crosswise between them.

2.

to 9, 2 to 10; 4 to 9, 4 to 10. Stick 9-10 also lies crosswise between stick 1-2 and stick 3-4.

5.

to 1, 5 to 2, 5 to 11, 5 to 9.

6.

to 3, 6 to 4, 6 to 11, 6 to 9.

7.

to 1, 7 to 2, 7 to 10, 7 to 12.

8.

to 3, 8 to 4, 8 to 10, 8 to 12.

5 Now go around it and tighten wires as much as you can. When you’re satisfied, twist all joints securely.

6 Tensegrity Sphere (See illustration, page 90)

7 Materials as for Tensegrity Icosa, but more of everything. You cut thirty sticks, each 9" long, and put a screw eye at each end.

8 322 | APPENDIX III MODEL MAKING

9 Cut thirty wires, each 5" long. Have five crayons ready, for color-coding as you go.

10 Drill a small hole straight through the midpoint of each stick, pass a wire through the hole, loop around and pass it through again, leave equal lengths hanging.

11 When you join two sticks, you always use the wire that passes through the center of a third. Call the crosswise stick in the middle of a joint the dangler. Length of wire, dangler to screw eye, should be about 11%". Twist surplus to fasten.

12 Make a pentagon--- five sticks, five danglers---and hang it from a shower-curtain rod with its top stick horizontal. Put a green mark on each of the five sticks of this pentagon.

13 The wire that passes through the top stick of the green pentagon now gets a stick at each end. Connect a dangler to each of these sticks, to each dangler another stick, to each stick another dangler. The free ends of the wires from these danglers are now joined to the dangler at the bottom of the green pentagon. You now have two intersecting pentagons. Code the five sticks of the new one red.

14 The dangler to the right of the top stick on the green pentagon goes to the middle of a top stick on the red pentagon. Code it blue, and work around, completing a blue pentagon. You’ll introduce three new sticks and incorporate another dangler near the bottom. This dangler is in the red pentagon, and goes to the middle of a stick on the green pentagon.

15 You should see the symmetry by now, and it’s easier to be guided by that than by instructions. Just keep color-coding the pentagonal rings and refer to the pictures in the text. Each pentagonal ring runs straight around the system; if it changes direction suddenly you’ve made a mistake. When you’re nearly done, the system will suddenly pull out into a spherical shape. When you’re finished, go around the sphere tightening wires till every stick is very slightly bowed and the system is springy but firm.

16 Geodesic Dome

17 The least bother is to order Kit Model #102 from Dome East, 325 Duffy Ave., Hicksville, N.Y. 11801; precut sticks plus con-

18 APPENDIX Ii: MODEL MAKING | 323 nectors and instructions. Or buy ‘‘D-Stix’’ rubber connectors from Edmund Scientific Co., Barrington, N.J. 08007. They cost about $3.50 for fifty. Order the six-sleeve type; forty will make a dome. You need ninety-two for a complete sphere. With these you use 14" dowel for struts. Cut with an X-acto knife as accurately as possible. Lengths are in centimeters, with connectors allowed for.

43 The easiest way to keep track is to paint them four different colors.

(1)

Pentagon subassembles. Five A’s radiate from a connector, leaving a sleeve unoccupied. Join ends with B’s. The pentagons will be slightly saucer-shaped. Make six, using up all the A’s and B’s.

(2)

Star subassembles. Six C’s radiate from a connector. Make five.

(3)

Final assembly. Lay a pentagon on the table, and surround it with the five stars. Join two adjacent rays of each star to the pentagon, so they make a triangle with the pentagon side. Fill the empty sleeve at each pentagon corner with a D. The five remaining pentagons go on the ends of the D’s, the D lined up with a pentagon spoke. Join the loose ends of the stars to the upper corners of these pentagons. The remaining D’s close the bottoms of the stars, with the remaining C’s for base ring and triangulated infill.

44 You now have a 14-sphere dome. A’s and D’s outline the icosa- hedral triangles, each edge divided into thirds (so this is called a three-frequency dome). Since it also sits flat, it’s called a truncatable. Most geodesics won’t sit flat except along the equator of the parent sphere. The calculations for this version were done by R. Ashworth and Tony Pugh of the Southern Illinois University Department of Design.

45 For more geodesic models see Domebook 2.