属于这一类的多面体骨架（和实体）被称为单稳单态多面体 (Domokos et al. 2020, Varkonyi and Domokos 2006a, Domokos and Kovács 2023)。虽然均质、单稳单态多面体实体的存在已被证明 (Lángi 2022)，但尚无已知示例 (Domokos and Kovács 2023)。然而，Domokos 和 Kovács (2023) 描述了一个单稳单态 0-多面体（即质量均匀分布在其顶点上的多面体）的示例，该多面体具有 21 个面和 21 个顶点，如上图所示。
Domokos, G. "My Lunch with Arnold." Math. Intell.28, 31-33, 2006.Domokos, G. and Várkonyi, P. L. "Geometry and Self-Righting of Turtles." Proc. Roy. Soc. B275, 11-17, 2008. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2562404/?tool=pmcentrez.Domokos, G. and Kovács, F. "Conway's Spiral and a Discrete Gömböc with 21 Point Masses." Amer. Math. Monthly130, 795-807, 2023.Domokos, G.; Kovács, F.; Lángi, Z.; Regős, K.; and Varga, P. T. "Balancing Polyhedra." Ars Math. Contemp.19, 95-124, 2020.Lángi, Z. "A Solution to Some Problems of Conway and Guy on Monostable Polyhedra." Bull. London Math. Soc.54, 501-516, 2022.Rehmeyer, J. "MathTrek: Can't Knock It Down." Apr. 5, 2007. http://sciencenews.org/view/generic/id/8383/title/Cant_Knock_It_Down.Sloan, M. L. "An Analytical Gomboc." 19 Jun 2023. https://arxiv.org/abs/2306.14914.Várkonyi, P. L. and Domokos, G. "Static Equilibria of Rigid Bodies: Dice, Pebbles and the Poincaré-Hopf Theorem." J. Nonlin. Sci.16, 255-281, 2006a.Várkonyi, P. L. and Domokos, G. "Mono-Monostatic Bodies: The Answer to Arnold's Question." Math. Intell.28, 34-38, 2006b.
, 
和 
, 
处分别具有唯一的稳定和非稳定平衡点。这里 
是一个小的正常数，其中 
似乎就足够了 (Sloan 2023)。![r^4=1+4betasinphicos[theta-(3pi)/2(cosphi-(cos^3phi)/3)],](/images/equations/Gomboc/NumberedEquation2.svg)
, 
和 
, 
处分别具有唯一的稳定和非稳定平衡点。这里，
是一个小的正常数，其中 
似乎就足够了 (Sloan 2023)。