Monostatic polytope

In geometry, a monostatic polytope (or unistable polyhedron) is a d-polytope which "can stand on only one face". They were described in 1969 by J.H. Conway, M. Goldberg and R.K. Guy. The monostatic polytope in 3-space they constructed has 19 faces. In 2012, Andras Bezdek has discovered an 18 face solution and, in 2014, Alex Reshetov has published a 14 face object.

Definition

A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet.

Properties

See also

References


External links

This article is issued from Wikipedia - version of the Friday, January 29, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.