The Conway-Guy polyhedron, illustrated above, is the name given by Domokos and Kovács (2023) to the 19-face 34-vertex polyhedral solid independently found by Guy (1968; Conway et al. 1969) and Knowlton (1969) which is stable on just its bottom face, shown in yellow above. The dimensions of the polyhedral solid can be varied by changing the lengths of the bottom rectangular face and the top ridge, though only some combinations are unistable.
This solid remained the smallest known unistable polyhedron until the discovery of an 18-face 18-vertex polyhedral solid by Bezdek (2011).
The Conway-Guy polyhedron illustrated above with parameters and in the parametrization of Hafner (2014) will be implemented in a future version of the Wolfram Language as PolyhedronData["ConwayGuyPolyhedron"]. Before scaling to unit minimum edge length, these correspond to ridge length and bottom rectangle length . For , this gives the smallest possible integer resulting in a unistable polyhedron.