Well I already went to the trouble so I'll go ahead and post mine as well.
To build against the back wall on the west side you have to allow for 2 free tiles of space. For the east side you *can* build right up to the edge of the east side of the plot, but you can't get on the stairs this way or build a wall. You can swap the direction the lowest steps are coming from so that you can get on the stairs, but there is still the wall issue.
In order to be able to get on the steps and walk past any wall you need to allow at least 2 free tiles of space from the east side.
Wah-lah.
Keep in mind that the first level of the stairs cannot be deleted by placing a teleporter underneath it, it must be deleted by removing any other stairs that have been built that fall in it's path. So you have to build the stairs to remove those parts of the stairs before you build the actual stairs that you want.
Building a spiral staircase on the north-west side:
1. Yellow = lowest tier, tier 1
brown = second lowest tier, tier 2
blue = third lowest tier, tier 3
red = highest tier, tier 4
Place three teleporters south of tier 1.
2. Place a south facing staircase on top of the yellow tile and all the teleporter pads.
3. Click twice on the transparency level for that floor to make the staircase transparent and erase the teleporters. Click the floor level you are on.
4. Place 2 teleporter pads to the west of the brown tile.
5. Place a west facing staircase so that it's first tier is south of the first tier of the stairs to be built.
6. Click twice on the transparency level and delete the 2 teleporters. Click the floor level you are on.
7. Erase the northern tier 1, this will also remove the southern tier 1.
8. Place three teleporter pads in a southern row to the east of the tier 2 stairs.
9. Place a south facing staircase so that it covers the teleporter pads except for its first tier.
10. Click twice on the transparency level and delete the 3 teleporters. Click the floor level you are on.
11. Place teleporter pads 1 north and 2 south of the blue tile, then 2 to the east of the southernmost tile.
12. Place a staircase so that all the southern tiles are covered, and the first tier of the staircase is not over a teleporter.
13. Click twice on the transparency level and delete the 3 teleporters that this new staircase is covering. Click the floor level you are on.
14. Place a staircase so that it covers the 2 remaining teleporter pads and the blue tile, leaving its first tier not over a teleporter.
15. Click twice on the transparency level and delete the 2 teleporters that this new staircase is covering. Click the floor level you are on.
16. Delete the southeasternmost tier 1 staircase in order to remove the westernmost tier 1.
17. Click twice on the transparency level and place the five teleporters in the corner to the west of the red tile and south. Click the floor level you are on.
18. Place a staircase so that it covers the three westernmost teleporter pads, except with it's tier one.
19. Click twice on the transparency level and delete the three teleporters this new set of stairs is covering. Click the floor level you are on.
20. Place a east facing set of stairs so that the two teleporter pads and the red tile are covered by stairs, and the tier 1 of this set of stairs is not covering any teleporters.
21. Click twice on the transparency level and delete the two teleporters this new set of stairs is covering. Click the floor level you are on.
22. Erase the southwesternmost tier 1 in order to get rid of the northwesternmost tier 1.
23. Place the shortest walls next to tier 1 and 2, the medium height walls in between tier 2 and 3, and the tallest walls next to tier 3 and 4.
24. It can also be made into a corner. Remember when you put the goza mat down between tier 2 and 3 it will need to be raised high enough to allow you to walk on it, which will leave a gap. Placing an additional goza mat that is one level (in the housing tool) lower than the first mat will cover this gap.