Bing's house

This is a famous example in topology called "Bing's house," named for R. H. Bing who created it. It is a house with two rooms. You enter the top room from the bottom face and the bottom room from the top face. If we view it as a 2-dimensional object (with 2-dimensional walls), Bing's house is a [contractible](https://en.wikipedia.org/wiki/Contractible_space) (here's a nice [sequence of illustrations](https://sketchesoftopology.wordpress.com/2010/03/25/bings-house/) showing that it is contractible), 2-dimensional simplicial complex that is not [collapsible](https://en.wikipedia.org/wiki/Collapse_(topology)). If we view the walls having thickness, then this is topologically (homeomorphic to) a 3-ball.

To make this object, print two copies of the rooms (one for upstairs and one for downstairs) and the floor between the rooms.