A supplement to Ian's answer: Here is the largest-area sofa known,
due to Gerver:
<hr />
![GerverSofa][1]
<hr />

> Gerver, Joseph L. (1992). "On Moving a Sofa Around a Corner". *Geometriae Dedicata* 42 (3): 267–283. ([Springer link](http://link.springer.com/article/10.1007/BF02414066).)

**Added** (triggered by @GeraldEdgar's remark).
The computational complexity of algorithms grows
exponentially in the dimension, about $n^5$ for
polyhedral objects with $n$ vertices moving in $\mathbb{R}^3$. 
Here is an algorithm moving an $n{=}4500$-triangle piano
through a challenging apartment requiring several tricky maneuvers:
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
![Piano][2]
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> Kuffner, James J., and Steven M. LaValle. "RRT-connect: An efficient approach to single-query path planning." *Robotics and Automation*, 2000. Proceedings. ICRA'00. IEEE International Conference on. Vol. 2. IEEE, 2000. 
([IEEE link](http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=844730&abstractAccess=no&userType=inst).)

Not surprisingly, the problem is also called *The Piano Mover's Problem*.


  [1]: https://i.sstatic.net/FBlms.png
  [2]: https://i.sstatic.net/le9JF.png