Don't know what an ice ball maker is, or how it works? Then check out the last page of this Instructable for a video of it in action.
You'll need access to a machine shop, and specifically a CNC machine. TechShop provides all the equipment you need for a monthy fee. I made it at TechShop, and you can too.
Ice ball makers work by melting a large block of ice into the proper shape. It accomplishes this by having two large blocks of aluminum (aluminum has high heat conductivity and capacity), each with a hemisphere carved into a side, slide together to form a single continuous chamber on the inside. What's left is a perfect sphere.
Step 1: Materials and Equipment
You'll need blocks that are in total at least 10 times the volume of your sphere. This is so the aluminum properly melts away the rest of the block. My ice ball maker produces 70 mm diameter ice balls, and the aluminum blocks are each 125x125x75 mm. That's a 13-to-1 ratio, and works pretty well.
You'll also need stainless steel rod. These serve as the bottom vertical guide shafts. I used 3/8" SS rod.
Last, you'll need plastic rod of a larger diameter. This piece slides over the stainless steel rod. I used 3/4" teflon rod, but teflon turns out to be hard to machine. I hear that Delrin machines well.
The only extra material is whatever you think will make the final product easy to use. I added rubber feet and a cabinet knob for lifting the top.
For equipment, you'll need a CNC mill and a lathe, and basic tooling. The inner hemispheres will be cut with a ball end mill, and you'll want as large a diameter here as possible. I used a 1" ball end, but smaller diameters will work as well. You'll also need a tap and die set.