Cutting the d-cube
Jim Lawrence · Journal of Research of the National Bureau of Standards · 1979
Som e probl e ms co ncern ed with cutting fa ces of th e cube with a ffin e or lin ea r s paces a re co ns ide red.It is s hown th at through a ny d-3 points of Rd the re passes a hype rplane whi c h c uts a ll the facets of th e d-c ube .Furthe rmore, it is s hown that if m < d -l and d' < d -[ (m + 1) /3], the n no m-d imens iona l a ffin e subspace of Rd c ut s all the d' -dimens iona l faces of the c ube.