Monostatic simplexes. III (Q5933871)

A polytope is called monostatic if its center of gravity is above only one facet. The authors show that in eight or fewer dimensions no monostatic simplex exists. In ten dimensions there is one, but there is none which falls sequently onto all its facets. [For part I and II of this paper see \textit{R. J. MacG. Dawson}, Am. Math. Mon. 92, 541-546 (1985; Zbl 0578.52006) and \textit{R. Dawson, W. Finbow} and \textit{P. Mak}, Geom. Dedicata 70, No.~2, 209-219 (1998; Zbl 0910.52007)].