Sections of a hypercube
This interactive animation shows the various polyhedra (on the left) that can be obtained by cutting a hypercube (on the right) with a hyperplane.
Four privileged directions are put in evidence (buttons on the left in the bottom): a hyperplane perpendicular to the line that goes through the centres of opposite (cubic) cells, a hyperplane perpendicular to the line which goes through the centres of opposite (square) faces, a hyperplane perpendicular to the line which goes through the midpoints of opposite edges, a hyperplane perpendicular to the line that goes through opposite vertices. You can also move the cube up and down with a click and drag.
Another animation shows the analogous situation on a cube.
animazione di Gian Marco Todesco
The image belongs to the sections...:
4D geometry (Animations)
Animations of the exhibitions (From the exhibitions of matematita)
Sections of a hypercube (4D geometry)