by pat » Wed Jul 26, 2006 8:07 pm
A solid tetracube would be a solid shape intersected with 3-d. The tessaract is a projection of a tetracube down to 3-d... it is not the intersection of a tetracube and 3-d.
Consider the 2-d analogy. If you took a 3-cube and intersected it with a plane, you would get, depending on how exactly you touched it to the plane, a point, a line, a triangle, a quadrilateral, a pentalateral, or a hexalateral. None of them would have lines crossing in the middle. They'd either be just the solid shape or just the outline of the shape (depending on whether your cube were solid).
On the other hand, there are many projections of 3-cubes down to 2-d that have intersecting lines and all manner of perspectives.