The proper names are:
1. Gateway Arch (in St.Louis)
2. United States Air Force Memorial (in Arlington, VA)
3. Atomium (in Brussels)
4. Cloud Gate (in Chicago)
5. The Kelpies (at The Helix in Scotland)
6. Unisphere (in Flushing Meadows, NY) - credit to Len for this one!
The common characteristic of these is that they are:
made out of stainless steel.
The book cipher is described as follows:
It encodes the name of subject 6 by using the names of the first 5 subjects. The first number X in parentheses represents the name of subject X, and the second number Y represents the Yth letter from the end of the name.
So we have:
* (4, -6) = the 6th letter from the end of "Cloud Gate" = U
* N
* (3, -3) = the 3rd letter from the end of "Atomium" = I
* (5, -1) = the 1st letter from the end of "The Kelpies" = S
* (5, -4) = the 4th letter from the end of "The Kelpies" = P
* (1, -1) = the 1st letter from the end of "Gateway Arch" = H
* (1, -8) = the 8th letter from the end of "Gateway Arch" = E
* (2, -4) = the 4th letter from the end of "United States Air Force Memorial" = R
* (2, -7) = the 7th letter from the end of "United States Air Force Memorial" = E
That spells out Unisphere.