In topology, the house with two rooms or Bing's house is a particular contractible, 2-dimensional simplicial complex that is not collapsible. The name was given by R. H. Bing.Bing, R. H., Some Aspects of the Topology of 3-Manifolds Related to the Poincaré Conjecture, Lectures on Modern Mathematics, Volume 2, 1964
The house is made of 2-dimensional panels, and has two rooms. The upper room may be entered from the bottom face, while the lower room may be entered from the upper face. There are two small panels attached to the tunnels between the rooms, which make this simplicial complex contractible.
See also
Dogbone space, another topological example constructed by Bing Dunce hat (topology), another space that is contractible but not collapsible List of topologies
External links Bing's house with two rooms at Info Shako A 3D model of Bing's house - the model can be visualized by using anaglyph glasses A printable 3D model of Bing's house at Thingverse
References