Monostatic polytope geometry , a monostatic polytope 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 discovered an 18 face solution , and in 2014 , Alex Reshetov 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 has an orthogonal projection in the interior of only one facet.Properties
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