Homogeneous, Monostatic Lattice Polyhedra, or the Magic Pyramid with 17 Sides

This paper presents the explicit geometric realisation of all monostatic polyhedra, the existence of which has been previously proven. Two of them are mono-unstable, denoted as P 2 and P 3 in Domokos et al. (2020), where their existence was proven. The other two ( P C and P B ) are monostable, and their existence was proven in Goldberg–Guy (1969) and Bezdek (2011), respectively. The combinatorial structure is identical for three of them, P 2 , P 3 and P B : it is a 17-sided pyramid. For each construction, we provide integer coordinates.