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This instructable shows how to make an expanding and contracting sphere out of K'nex construction toys.  The design is similar to that of the toy sold as the "Hoberman Sphere".  (Note: the original US patent on the Hoberman sphere was issued in 1991 and is now expired.)  In addition to being fun to build and fun to play with, it offers interesting lessons in mathematics.

Watch the K'nex sphere in action:

To make the sphere, you will need the following K'nex parts:
  • 96 grey 2-slotted connectors
  • 96 red 3-slotted connectors
  • 96 green 4-slotted connectors
  • 192 yellow rods
  • 96 tan clilps
  • 96 short white rods
  • 96 blue spacer rings
  • 48 short green rods
  • 12 white 8-slotted hubs
Yep, that's a lot of K'nex.  If you don't have everything on the list you can make some substitutions.  

You can use any color rods instead of the yellow rods, just as long as they're all the same length.  I've made the model using blue rods -- it's smaller and not as pretty but it's sturdier because it weighs less.  I wouldn't recommend longer rods, though -- it might fall apart under the extra weight.

You can also substitute red connectors for some of the grey ones by ignoring the extra slot, but you have to be careful how you orient them or they can limit the range of motion of the model.  

The white connectors and green rods can be left out, too, but you'll have to do something else to stabilize the "hubs" in Step 4 -- like inserting a blue rod as a diagonal brace (you'll see when you get there).

The blue spacers are also optional, but they really help keep the model moving smoothly and I strongly recommend using them if you can.

Step 1: Making rhombuses

Remember rhombuses from math class?  A rhombus is a quadrilateral with four equal length sides.  Use all the yellow rods and the grey and green connectors to build 48 of them.  The acute (sharp) angle in these rhombuses is 45 degrees and the obtuse (shallow) angle is 135 degrees.

After you've made all the rhombuses (Latin snobs call them "rhombi"), link them together in pairs by adding a clip to the end of a white rod, slipping the rod through the center of a green hub, add a blue spacer, then another rhombus (through the green hub again) and topping it off with another clip.

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