in the euclidean plane, it is possible to divide any area or measure into four equal subsets, using the ham sandwich theorem. similarly but more complicatedly, any volume or measure in three dimensions may be partitioned into eight equal subsets by three planes. however, this result does not generalize to five or more dimensions, as the moment curve provides examples of sets that cannot be partitioned into 2 subsets by "d" hyperplanes. in particular, in five dimensions, sets of five hyperplanes can partition segments of the moment curve into at most 26 pieces. it is not known whether four-dimensional partitions into 16 equal subsets by four hyperplanes are always possible, but it is possible to partition 16 points on the four-dimensional moment curve into the 16 orthants of a set of four hyperplanes.