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The parts from the kit: 6 sticks, 7 elastic bands, and 13 end caps.
Place one band on each stick. The loops should not be twisted.
Place 2 of the sticks as sides of an "H". Put one stick below and one above the two side sticks at approximately the mid-point of the vertical sticks. The two horizontal sticks should be right on top of each other.
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Secure the horizontal sticks by placing the end caps over them. The end caps need to be pushed on tightly enough so that none of the slot is visible and the capped end will not slide at all.
Add one stick to the top of the middle of the H and one to the bottom of the H. The sculpture will become 3-dimensional at this point.
The same shape from a different angle.
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Place end caps on the two pieces that you just added. Hook one strap from the band around the upper center stick to the upper slot on the left stick.
Hook one strap from the band around the lower center stick to the lower slot on the left stick.
Hook one strap from the band around the upper center stick to the upper slot on the right stick.
Hook one strap from the band around the lower center stick to the lower slot on the right stick
Your tensegrity should look similar to this picture. Cap the last 4 end-points.
True your structure. Do this by loosening all 12 end caps slightly. You should be able to slide the end freely. If you connected the pieces close to the middle of the elastic band, your tensegrity icosahedron will probably be very close to true. I suggest deliberately unbalancing the structure and practicing truing it. This image shows an icosahedron that has been deliberately unbalanced.
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Congratulations! You have a completed and trued tensegrity icosahedron. You should have one extra cap and one extra strap; put these spares back in the box for safe-keeping.