If an ellipse has two radiuses, is there something like it, but with three or more radiuses?

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If we say that a circle has one radius, and an ellipse has two, can I define figures that have three, four, or more radiuses?

Also, how can I get that "radius"? In an ellipse that is 10 at its shortest, and 20 at its longest, obviously, at 0°, the "radius" is 10, and at 90° it's 20(well, depends on its angle I guess), is there a formulate I can use to calculate that?

Not particularly knowledgeable about math, hope my question makes sense.

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One answer to your question is provided by an ellipsoid, a three dimensional version of an ellipse, which has three 'radii.' See: http://en.m.wikipedia.org/wiki/Ellipsoid

You also asked for an equation to measure the radius at any angle - for that, see here, the section "Polar form relative to center." http://en.m.wikipedia.org/wiki/Ellipse