:::1.  So to be clear, the "triangles" and "squares" really do have smaller angles, and at any given point there are only 360 degrees.  But, say, if you shine a light down one of the lines of the triangle it will end up going "straight" to the next vertex?  And you could tile our universe with these "tetrahedrons" and "cubes", three cubes around the vertex of a tetrahedron, three tetrahedrons around the vertex of a cube, for a total of I think three cubes and four tetrahedrons meeting at a point?  Is there a way to calculate how big the side of each polytope is? 

 :::2. OK, so the anti-de Sitter space is the physical dimensions of our space (not time) ... plus the compactifed dimensions?  And time remains a separate dimension orthogonal to everything else, and not subject to any transformations. 

 :::3. The boundary of the two dimensional space is a cylinder (counting the time dimension); in space it is a line that wraps around on itself, and the boundary of the four dimensional space would be a three dimensional space that wraps around on itself?  Is the geometry/manifold specified by the theory?  And if an infinite anti-de Sitter space has a boundary of finite size, what determines the size of the boundary?  I still am confused at what actually "lives" in the anti-de Sitter space.  Given the lack of precision of measurements in our space, what is this apparently "infinite resolution" needed for?  (I'm waaay out to sea by now, distant ship smoke on the horizon...)