Editing 5-cell (section)

===Projections===
[[Image:Stereographic polytope 5cell.png|240px|thumb|[[Stereographic projection]] wireframe (edge projected onto a [[3-sphere]])]]

The A<sub>4</sub> Coxeter plane projects the 5-cell into a regular [[pentagon]] and [[pentagram]]. The A<sub>3</sub> Coxeter plane projection of the 5-cell is that of a [[square pyramid]]. The A<sub>2</sub> Coxeter plane projection of the regular 5-cell is that of a [[triangular bipyramid]] (two tetrahedra joined face-to-face) with the two opposite vertices centered.

{{4-simplex Coxeter plane graphs|t0|150}}

{|class="wikitable" width=640
!colspan=2|Projections to 3 dimensions
|- valign=top align=center
|[[Image:Pentatope-vertex-first-small.png]]<BR>The vertex-first projection of the 5-cell into 3 dimensions has a [[tetrahedron|tetrahedral]] projection envelope. The closest vertex of the 5-cell projects to the center of the tetrahedron, as shown here in red. The farthest cell projects onto the tetrahedral envelope itself, while the other 4 cells project onto the 4 flattened tetrahedral regions surrounding the central vertex.
|[[Image:5cell-edge-first-small.png]]<BR>The edge-first projection of the 5-cell into 3 dimensions has a [[triangular dipyramid]]al envelope. The closest edge (shown here in red) projects to the axis of the dipyramid, with the three cells surrounding it projecting to 3 tetrahedral volumes arranged around this axis at 120 degrees to each other. The remaining 2 cells project to the two halves of the dipyramid and are on the far side of the pentatope.
|- valign=top align=center
|[[Image:5cell-face-first-small.png]]<BR>The face-first projection of the 5-cell into 3 dimensions also has a triangular dipyramidal envelope. The nearest face is shown here in red. The two cells that meet at this face project to the two halves of the dipyramid. The remaining three cells are on the far side of the pentatope from the 4D viewpoint, and are culled from the image for clarity. They are arranged around the central axis of the dipyramid, just as in the edge-first projection.
|[[Image:5cell-cell-first-small.png|320px]]<BR>The cell-first projection of the 5-cell into 3 dimensions has a tetrahedral envelope. The nearest cell projects onto the entire envelope, and, from the 4D viewpoint, obscures the other 4 cells; hence, they are not rendered here.
|}