Polyhedra project?

Question

we have to build a polyhedra in geometry class using AT LEAST two of the following shapes; a regular hexagon, a regular pentagon, a regular square, or a regular triangle. It cannot be a prism. one example would be an Icosidodecahedron.

picture - http://upload.wikimedia.org/wikipedia/en/0/02/Icosidodecahedron.png

so my question is, is there a online step by step guide on how to build one? it doesnt matter if its easy or hard, if it takes a long time or not, or if it uses two of the polygons, three, or all four. all i need is a step by step guide on how to make one, or like a list of how many faces and what types i need. anything that you think would help me, post it here.

Answer 1

I've put a couple of links to nets below

The truncated tetrahedron is a nice easy one (This is what you get if you cut off the points of a tetrahedron). The truncated octahedron is a bit more involved.

If you want to make your own net the easiest way is to draw a net on paper or use a computer program to draw one and print it out. (All the sides will be the same length unless you are doing something complex.) You also need to add tabs for gluing - the source below doesn't have any but you can easily add some by hand as they don't have to be exact.

You need to add tabs on half the faces that aren't already connected. You have to work out where each tab will go when the model is folded and *not* put a tab on the other face. If that is tricky, put on extra tabs then cut them off when you find you don't need them.

You can do a model with paper or thin card. Avoid very thin paper as the sides tend to buckle and the flaps show. Cut it out carefully. You might find it easiest to use a craft knife and a steel ruler if using card. (Make sure you put a craft mat underneath so you don't destroy the table!) Only cut around the outside. Next you need to make creases where all the polygons meet, and on all the tabs where they meet the edge of a polygon. If you are using card you may need to score using something blunt along the lines first.

You then glue your model together using paper glue, gluing the tabs to what will be the inside of the model. Ideally you want a glue that is reasonably sticky so things don't spring apart, but allows some repositioning. If you can only get a thin gum that takes a while to dry and doesn't stick well until then, use some clothes pegs to keep your model together.

If your model uses triangles, you may need to trim some of the tabs at the ends so that they don't overlap. The final flap is the hardest as you can't get inside the model easily to apply pressure. You can either hope, or perhaps use a thin wire in a corner to apply some pressure. (Or if the edge is very acute you could try gently squeezing and hoping you can get the model back into shape afterwards.) Leave your model so its glue can set before handling it too much.

An alternative to making a net is to cut out individual faces all with tabs on each side. You then glue tabs to tabs. This doesn't look quite as good in my opinion as the edges tend to have a gap.

Oh and if you want to make a ball with hexagons you will need twelve pentagons, or triangles arranged to act a a pentagon. Will need a lot of faces though.

Have fun!