Pop-Up Icosahedron


Instructions for making a popup octahedron and a pop-up dodecahedron are given in Johnny Ball's Think Box (Ball, 1982). The octahedron works well, though the dodecahedron is rather unsatisfactory since it requires an elastic bank on the outside, and doesn't always popup neatly. The icosahedron described below has the elastic bands on the inside, and pops up neatly (almost) every time. Other more intricate designs for pop-up polyhedra are given by Johnson & Walser (1997).

Design Details

You'll need to make two copies of the net shown below, with both having the same handedness. It is best to use card and score the fold lines. The two copies will eventually be put back to back, with the three pairs full-length tabs folded over and stuck to each other.

Before assembling the two halves, you need to make holes in the six half-length tabs to allow elastic bands to be inserted. These should be close to the square end, and have a slit out towards the slanted side to get the band in. The slit should be positioned so the bands won't naturally come back out, but it can also be taped up for good measure.

You then need to stick the two halves together and fit elastic bands between the holes. You'll need three bands, linking pairs of opposite tabs. You need to find bands which are still slightly stretched when the icosahedron is 'popped up', yet are stretchy enough to allow it to be squashed flat. The availability of such bands may need to influence the size of your model.

The way the bands cross over each other in the middle is crutial. They must be arranged to ensure that when the adjecent tabs come towards each other, the square ends of the half tabs are forced together to hit each other. It is this hitting which prevents the model from popping too far. You may find that it helps to add some tape over the square edge of the half-tabs covering a bit of the bands. This will smoothly join the band to the tab, and ensure everything ends up in the right place.