Sections of Hyper-Cube in Five Dimensions

Hiroshi Fukuda, Nobuaki Muto, Kikuko Goto and Gisaku Nakamura

School of Administration and Informatics,

University of Shizuoka, Shizuoka-shi, Shizuoka 422, Japan

We report on sections of a hyper-cube in five dimensions. There are 484 different sections except for isomorphism. We enumerate them by creating spanning subgraphs of the hyper-cube. Several simple necessary conditions for the spanning subgraphs to be pieces of a hyper-cube divided by the sections have been found to be also sufficient conditions in the case of N dimensions with N \le 5.