House with two rooms or Bing's house is a particular
contractible, 2-dimensional
simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial ...
that is not
collapsible. The name was given by
R. H. Bing
R. H. Bing (October 20, 1914 – April 28, 1986) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His father was named Rupert Henry, but Bing's mother thought that "Rupert Henry" was too ...
.
[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
*
Dunce hat
*
List of topologies
External links
Bing's house with two rooms at Info ShakoA 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
Low-dimensional topology
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