Editing 5-cell (section)

=== As a Boerdijk–Coxeter helix ===
[[File:5-cell 5-ring net.png|480px|thumb|The 5-cell Boerdijk&ndash;Coxeter helix]]
A 5-cell can be constructed as a [[Boerdijk–Coxeter helix]] of five chained tetrahedra, folded into a 4-dimensional ring.{{Sfn|Banchoff|2013}}{{Failed verification|date=March 2025|reason=Banchoff 2013 describes the decomposition of the 8-cell and 24-cell into tori, but neither discusses the 5-cell nor anything relating to Boerdijk–Coxeter helices.}} The 10 triangle faces can be seen in a 2D net within a [[triangular tiling]], with 6 triangles around every vertex, although folding into 4-dimensions causes edges to coincide. The purple edges form a [[pentagon#Regular pentagons|regular pentagon]] which is the [[Petrie polygon]] of the 5-cell. The blue edges connect every second vertex, forming a [[pentagram]] which is the ''Clifford polygon'' of the 5-cell. The pentagram's blue edges are chords of the 5-cell's ''isocline'', the circular rotational path its vertices take during an [[Rotations in 4-dimensional Euclidean space#Double rotations|isoclinic rotation]], also known as a [[Rotations in 4-dimensional Euclidean space#Isoclinic rotations|Clifford displacement]].