rhombic zonohedra
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These are polyhedra where every face is a rhombus. I initially got excited about them when making the model made out of playing cards on the right. It is a rhombic triacontrahedron, which is the dual of a rhombicosadodecahedron! You can see this duality by looking at the dots on the back of the cards in the picture below.
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Zometool is a great way of investigating these shapes.
The picture on the right is the same object as the card model above. Each red strut is a card! There are other rhombic zonohedra - the rhombic dodecahedron is one. There are others - below is a picture of a rhombic enneacontrahedron. 
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They are lovely models to make using zometool, which is hardly surprising seeing as though making these is why it was invented - the word zome is a concatentation of the words zone and dome.
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Why are they called zonohedra? Well, each of these models has 'zones' which are bands of faces sharing parallel edges. You can follow parallel edges around the shape - they form equators of faces. If you look at the red model above, the zones have 10 faces in each. There are 6 of them in total. Each face is in two zones, giving 6 x 10 / 2 faces on the shape in total.
The yellow one (when complete) will have 10 zones of 18 faces each, giving the total number of faces as 90!
The number of zones is the number of different directions of edges in the shape. If you take one ball and put in struts to represent all the different directions of edges (called a star), you will find the number of zones in the shape.
The yellow one (when complete) will have 10 zones of 18 faces each, giving the total number of faces as 90!
The number of zones is the number of different directions of edges in the shape. If you take one ball and put in struts to represent all the different directions of edges (called a star), you will find the number of zones in the shape.