屬於這一類的多面體骨架（和實體）被稱為單穩單態多面體 (Domokos et al. 2020, Varkonyi and Domokos 2006a, Domokos and Kovács 2023)。雖然均質、單穩單態多面體實體的存在已被證明 (Lángi 2022)，但尚無已知示例 (Domokos and Kovács 2023)。然而，Domokos 和 Kovács (2023) 描述了一個單穩單態 0-多面體（即質量均勻分佈在其頂點上的多面體）的示例，該多面體具有 21 個面和 21 個頂點，如上圖所示。
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 
, 
處分別具有唯一的穩定和非穩定平衡點。這裡 
是一個小的正常數，其中 
似乎就足夠了 (Sloan 2023)。![r^4=1+4betasinphicos[theta-(3pi)/2(cosphi-(cos^3phi)/3)],](/images/equations/Gomboc/NumberedEquation2.svg)
, 
和 
, 
處分別具有唯一的穩定和非穩定平衡點。這裡，
是一個小的正常數，其中 
似乎就足夠了 (Sloan 2023)。