A Sliceform tetrahedron

See also the posts on how to make and assemble the models and Sliceform templates and Downloads

This Sliceform is available in two versions, a simple one which takes about 10 minutes to cut out and assemble since it has only six slices and a more advanced one which has 18 slices and takes about an hour to make.

You should make the 10 minute one before attempting the advanced one.

How the model is designed

This model has been designed by taking a tetrahedron in a cube like this:

and making two sets of slices, one horizontal and one vertical, parallel to sides of the cube.

These slices are all rectangles. See at the end of the post  for why. It should help you to assemble the tetrahedron Sliceform.

The 10 minute tetrahedron template

Download the file you want for printing and use that to create the model. The following graphic is to help you understand what the slices look like.

The slices for half of the model look like this:

A single page of the template contains slices to make four tetrahedra. Make two copies, each on different coloured card and mix the different coloured slices for different effects, to give eight variations on the tetrahedron. Start by making all slices in each direction a different colour.
See How to make and assemble the models for general printing instructions for printing or copying onto card.

Assembling the 10 minute tetrahedron

See the post on how to make and assemble the models for more about cutting out and cutting the slots. Take extra care with the slots.

The simple model only has six slices. The two central squares that correspond to the squares in the design model and two other slices in each direction.

Since there are only a few slices, cut out all the pieces and cut the slots on each one.

Fit the centre squares together, then add the other two slices in each direction. Use the two half tetrahedron models to judge how they are orientated. Think symmetrically.

When you have made the model, fold it flat in two directions.

The advanced tetrahedron template

Download the file you want for printing and use that to create the model. The following graphic is to help you understand what the slices look like.

The slices for half of the model look like this:

A single page of the template contains slices to make one tetrahedra. Make two copies, each on different coloured card and use one colour in each direction to make two models.

See the post on how to make and assemble the models and Sliceform templates and Downloads for the general instructions for printing or copying onto card.

Assembling the advanced tetrahedron model

This model has many more pieces and takes up to an hour to make. With more slices the tetrahedron looks more solid.

Make the simple model first so that you can see the structure when you are making this one.

Take extra care not to cut the slots too wide or you will find that the pieces fall out in the early stages of assembly. You will probably find it easier to cut pairs of slices and then fit them onto the model.

Cut out the central squares and their slots and fit them together. Then cut the next four slices (two in each direction) and add them to your model. Continue cutting and adding four slices at a time until you reach the outside. If you make the model with two colours of card it will not only be a more interesting model, it will also be easier to make.

When you have made the model, fold it flat in two directions. With it folded, tap the long flat ends gently on a flat surface to distribute the slices evenly in the slots. Look at the patterns it creates.

The slices of a tetrahedron and why they are rectangles

This is a picture of a conventional net for half a tetrahedron.

Cut two versions out on paper and assemble them by sticking the tabs.

Placing the squares of the two halves together makes a tetrahedron (if you put them together with a 90 degree rotation).

The dotted lines show the position of slices for making the Sliceform.
Measure them and trace them round to see how the shapes of the rectangles change, from a long thin one at the edge, to a fatter one as the sides become equal in the central square. As you continue to the other half, they become longer and thinner again, but in the other direction.

It is a good idea to make this model to help you see how the rectangles of the Sliceform slot together.

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