# Quasitruncated Cuboctahedron

Just before starting the design of a new model I wanted to build this one, just because it looked like a very intresting model to me while I was browsing through Magnus Wenningers book "Polyhedron Models" for inspiration. The Quasitruncated Cuboctahedron is also called Great Truncated Cuboctahedron.

It can be observed easily that this model consists of squares (12) and octagrams (6). What is not so easy to see here is that the model also consists of hexagons (8). I gave half of these the colour yellow and the other half the colour blue. I the colour arrangement I choose, I tried to emphasize the fact that the octagrams and the squares lie in planes of three cubes, by using the one colour for the faces that lie in one cube. I also used colours that are alike: red, pink, and bordeaux-red. The hexagons with yellow and blue have very different colours. The arrangement of the yellow and blue is done so that each colour lies in a plane of a tetrahedron.

The amazing thing about this model is that it has an intrigate interior structure formed by the 8 hexagons. The interior structure consists of an octahedron and a stella octangula, where the octahedron is the base for the stella octangula. Of the latter the vertices are cut off so that 8 "caves" appear. Here you can see a picure of it, and here you see it with some faces glued on. In the model one can look into one of those through the triangular hole that was formed by this process of cutting off one vertex of the stella octangula. In the picture above I try to show that. One looks on the yellow triangle as part of the octahedron.

Oh, the thing on the right side is a tea bag. It is Yogi Tea Classic, one of my favorite teas. It is a kind of Indian tea, though the real one should be boiled some time with the herbs, instead of just using a tea bag.

Enthousiastic people that want to make a model of this one can download a template, though I have to warn that this is not a model for beginners. Not because it is difficult to build this one, but it not easy to understand which parts you should be put where. First I have a coloured template, in which you can see how the different parts lie in one plane. I also have a black and white print, which is easier to use as a template. The template can be used to prick holes at the vertices to be able to draw the pieces on cardboard. (Don't forget to use tabs inside.)

Some building tips.

• I began with the octahedron, leaving tabs sticking out to be able to add the "caves".
• Then I added the caves (consisting of the darker green faces in the coloured template). Remember to have the coloured sides on the inside!
• In the next step I added two parts that consisted of the center of a square and four side parts of a hexagon and then one octagram. I found it easier not to wait with the octagrams too long, since octagrams have many edges to glue.
• I found it best to add all parts consisting of two triangular sides of squares as last, since these do not have to many edges to glue.