Editing Hexagon (section)

== Dissection==
{| class="wikitable skin-invert-image" align=right style="text-align:center;"
! [[6-cube]] projection
!colspan=2| 12 rhomb dissection
|-
| [[File:6-cube t0 A5.svg|120px]]
| [[File:6-gon rhombic dissection-size2.svg|140px]]
| [[File:6-gon rhombic dissection2-size2.svg|140px]]
|}
[[Coxeter]] states that every [[zonogon]] (a 2''m''-gon whose opposite sides are parallel and of equal length) can be dissected into {{nowrap|{{frac|1|2}}''m''(''m'' − 1)}} parallelograms.<ref>[[Coxeter]], Mathematical recreations and Essays, Thirteenth edition, p.141</ref> In particular this is true for [[regular polygon]]s with evenly many sides, in which case the parallelograms are all rhombi. This decomposition of a regular hexagon is based on a [[Petrie polygon]] projection of a [[cube]], with 3 of 6 square faces. Other [[parallelogon]]s and projective directions of the cube are dissected within [[rectangular cuboid]]s.
{| class="wikitable skin-invert-image collapsible" style="text-align:center;"
!colspan=12| Dissection of hexagons into three rhombs and parallelograms
|-
!rowspan=3| 2D
! Rhombs
!colspan=3| Parallelograms
|- valign=top
|[[File:Hexagon_dissection.svg|80px]]
|[[File:Cube-skew-orthogonal-skew-solid.png|95px]]
|[[File:Cuboid_diagonal-orthogonal-solid.png|120px]]
|[[File:Cuboid_skew-orthogonal-solid.png|120px]]
|- valign=top
| Regular {6}
|colspan=3| Hexagonal [[parallelogon]]s
|-
!rowspan=3| 3D
!colspan=2| Square faces
!colspan=2| Rectangular faces
|- valign=top
| [[File:3-cube_graph.svg|95px]]
| [[File:Cube-skew-orthogonal-skew-frame.png|95px]]
| [[File:Cuboid_diagonal-orthogonal-frame.png|120px]]
| [[File:Cuboid_skew-orthogonal-frame.png|120px]]
|- valign=top
|colspan=2| [[Cube]]
|colspan=2| [[Rectangular cuboid]]
|}