Rhombicuboctahedron Area/Volume

[Shadow]

Hi all,

 

I put this in Applied Mathematics because I'm going to apply this in real life. I'll let you in on some background so you know why I'm asking.

Me and my friend are building a hookah. Since were artistic maniacs who are creatively anti-talented, we want the water jar to be in a shape of an incomplete rhombicuboctahedron.

The "incomplete" part is where this gets a little complicated. Since we can't levitate our hookah, and one of us holding it while the other one smokes is out of the question, we need it to be steady of course. So the actual shape of our hookah water jar will be as follows:

 

Take a normal rhombicuboctahedron. It's basically made of an Octagonal Prism, and then those two "things" attached above and below. The "things" are the part where, going around the rhombicuboctahedron, you would see a square, then a triangle, then a square and so on. And theres a square on the very top and bottom. To put it plainly; take away the Octagonal Prism, and what's left is what I'm talking about. Now, take away one of those "things" and put the rhombicuboctahedron back together. You kinda get half a rhombicuboctahedron, but not quite. This is the shape our water jar is supposed to have.

 

My problem lies in the area and volume of this incomplete rhombicuboctahedron. I know the equation for the area of a normal rhombicuboctahedron, but I don't know how it's formed (as in the equation) so I can't edit it to fit my needs with our water jar shape. The same thing goes for volume.

 

Could someone please tell me how the equation is formed, so I can make my own, or maybe even post the equation itself?

 

Thx

 

EDIT: Okay I just found out that the two "things" I was trying to describe are "square cupolae". Love you wiki :-*

[ronnyr]

Can't help you the equation I'm afraid. When you create it, please post a pic. And it looks cool, with your permission I'll post a pic on my site in the homemade hookah category.

 

It's a pretty cool idea.

[Shadow]

Sure thing Thanks.

 

I hope someone can help, cause I'm afraid we can't go much further until then...