A Zome is properly called a Polar Zonohedron, but it is quicker to write Zome.

It is somewhere between a dome, a cone, and a pyramid. It is made out of equal length lines arranged into "diamond" parallelograms, which are flat, so the area between the struts could be filled with flat glass. This zome I made is given rigidity by tensioning the "diamonds" with nylon along the diamond diagonals.

You can make a zome with any number of sides, but this one has 10.

Starting at the top arrange 10 struts equally spaced to form a 10 sided pyramid with a decagon at the base. If the lines are all horizontal you will end up with a flat zome. In this Zome I have made the diameter of the decagon equal to the strut length, which I believe gives an elegant shape.

Then complete a parallelogram for each pair of struts to get to the next level down. Note that each new level consists only of lines parallel and of equal length to the level above, so therefore each new "floor" is the same height below the one above. This would make this type of structure good for buildings.

There are other interesting properties, such as that the profile of a zome is approximately a sine curve. Also, if you continue adding levels you end up enclosing a vaguely onion or cigar shaped volume. The total number of floors is the same as the number of sides. ( My Zome is only half built. Imagine the other half as a reflection, but you can see it has 5 floors ). Another thing about zomes is that you can extend them. For other info about zomes  look on the internet.

It doesnt really matter what angle the top lines make with the horizontal. But if they are all horizontal you get a flat zome, and the more angled they are the thinner the zome.

So how do you work out the length of the diamond diagonals to achieve the correct zome look ? Lay the zome on its side and several things become obvious. Firstly the 3d-ness goes, and you may as well be looking at a flat zome. ( please ignore the distortion in the picture caused by perspective ). Starting with the fact that the angles at the center are Pi/5, and that all the lengths are the same, and using elementary geometry, you can find all the angles in the picture, and easily deduce that the diagonals of the diamonds correspond exactly in length with the diagonals of the inner decagon. In the picture on the right you can see how the lengths labelled 2, 3, 4 and 5 match up. I made the decagon at the base rigid by linking every other corner - ie the shortest diagonal, which by a similar method as before, I found to be twice the length of the inner diagonal labelled 4. So the whole thing can be built without any numeric calculation at all ! Fab. See the page on regular polygons for related info.

Stand underneath and look up. Cosmic !

Prototype Appollo module.