Editing 4-polytope (section)

==Visualisation==
{| class=wikitable align=right
|+ Example presentations of a [[24-cell]]
!colspan=2|Sectioning
![[Net (polytope)|Net]]
|- align=center
|colspan=2|[[File:24cell section anim.gif|200px]]
|[[File:Polychoron 24-cell net.png|150px]]
|-
!colspan=3|Projections
|-
![[Schlegel diagram|Schlegel]]
!2D orthogonal
!3D orthogonal
|- align=center
|[[File:Schlegel wireframe 24-cell.png|100px]]
|[[File:24-cell t0 F4.svg|100px]]
|[[File:Orthogonal projection envelopes 24-cell.png|150px]]
|}

4-polytopes cannot be seen in three-dimensional space due to their extra dimension. Several techniques are used to help visualise them.

;Orthogonal projection
[[Orthogonal projection]]s can be used to show various symmetry orientations of a 4-polytope. They can be drawn in 2D as vertex-edge graphs, and can be shown in 3D with solid faces as visible [[projective envelope]]s.
;Perspective projection
Just as a 3D shape can be projected onto a flat sheet, so a 4-D shape can be projected onto 3-space or even onto a flat sheet. One common projection is a [[Schlegel diagram]] which uses [[stereographic projection]] of points on the surface of a [[3-sphere]] into three dimensions, connected by straight edges, faces, and cells drawn in 3-space.

;Sectioning
Just as a slice through a polyhedron reveals a cut surface, so a slice through a 4-polytope reveals a cut "hypersurface" in three dimensions. A sequence of such sections can be used to build up an understanding of the overall shape. The extra dimension can be equated with time to produce a smooth animation of these cross sections.

;Nets
A [[Net (polytope)|net]] of a 4-polytope is composed of polyhedral [[Cell (geometry)|cells]] that are connected by their faces and all occupy the same three-dimensional space, just as the polygon faces of a [[net (polyhedron)|net of a polyhedron]] are connected by their edges and all occupy the same plane.