MathDB
Is it possible to choose a set of 100 points ?

Source:

September 30, 2010
geometry3D geometrysymmetryrotationIMO LonglistIMO Shortlistcube

Problem Statement

Is it possible to choose a set of 100100 (or 200200) points on the boundary of a cube such that this set is fixed under each isometry of the cube into itself? Justify your answer.