Editing 5-cell (section)

=== Geodesics and rotations ===
[[File:5-cell-orig.gif|thumb|A 3D projection of a 5-cell performing a [[SO(4)#Double rotations|double rotation]].]]
The 5-cell has only [[digon]] central planes through vertices. It has 10 digon central planes, where each vertex pair is an edge, not an axis, of the 5-cell. Each digon plane is orthogonal to 3 others, but completely orthogonal to none of them. The characteristic [[Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]] of the 5-cell has, as pairs of invariant planes, those 10 digon planes and their completely orthogonal central planes, which are 0-gon planes which intersect no vertices of the 5-cell.

Below, a spinning 5-cell is visualized with the fourth dimension squashed and displayed as colour. The [[Clifford torus]] is depicted in its rectangular (wrapping) form.

<gallery caption="[[Rotations in 4-dimensional Euclidean space#Visualization of 4D rotations|Visualization of 4D rotations]]">
File:Simple 4D rotation of a 5-cell, in X-Y plane.webm|loop|Simply rotating in X-Y plane
File:Simple 4D rotation of a 5-cell, in Z-W plane.webm|loop|Simply rotating in Z-W plane
File:Double 4D rotation of a 5-cell.webm|loop|Double rotating in X-Y and Z-W planes with angular velocities in a 4:3 ratio
File:Isoclinic left 4D rotation of a 5-cell.webm|loop|Left isoclinic rotation
File:Isoclinic right 4D rotation of a 5-cell.webm|loop|Right isoclinic rotation
</gallery>