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, R. K. Guy and K. C. Knowlton.

In 2012, Andras Bezdek discovered an 18-face solution,[1] and in 2014, Alex Reshetov published a 14-face polyhedron.

[2] 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.