Is there a 3 D equivalent of Geometer's Sketchpad?

I have Geometer’s Sketchpad at home and am happy with it as a way of working with ideas that I thought of or read about, but it I would like to be able to work in three dimensions.

As a bare minimum I would like to be able to do the following in addition to all the obvious carry-overs from 2 D geometry:

1. Plot points using x, y and z coordinates
2. Draw a sphere centered at a point
3. Create a plane determined by 3 points or a point and a line
4. Draw a line perpendicular to a plane or a plane perpendicular to a line at a specified point
5. Be able to select a plane and have my mouse movements confined to the plane and to be able to work with with regular 2D Geometer’s Sketchpad within the specified plane
6. Form a surface by rotationg a 2 dimensional shape

Is there a software package that allows me to do all these things that is easy to learn and not exporbitantly priced?