Editing Decagon (section)

==Dissection==
{| class=wikitable align=right
![[10-cube]] projection
!colspan=4|40 rhomb dissection
|- align=center
|[[File:10-cube t0 A9.svg|class=skin-invert-image|100px]]
|[[File:10-gon rhombic dissection-size2.svg|100px]]
|[[File:10-gon rhombic dissection2-size2.svg|100px]]
|[[File:10-gon rhombic dissection3-size2.svg|100px]]
|[[File:10-gon rhombic dissection4-size2.svg|100px]]
|- align=center
|[[File:10-gon rhombic dissection5-size2.svg|100px]]
|[[File:10-gon rhombic dissection6-size2.svg|100px]]
|[[File:10-gon rhombic dissection7-size2.svg|100px]]
|[[File:10-gon rhombic dissection8-size2.svg|100px]]
|[[File:10-gon rhombic dissection9-size2.svg|100px]]
|}
[[Coxeter]] states that every [[zonogon]] (a 2''m''-gon whose opposite sides are parallel and of equal length) can be dissected into ''m''(''m''-1)/2 parallelograms.<ref>[[Coxeter]], Mathematical recreations and Essays, Thirteenth edition, p.141</ref>
In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the ''regular decagon'', ''m''=5, and it can be divided into 10 rhombs, with examples shown below. This decomposition can be seen as 10 of 80 faces in a [[Petrie polygon]] projection plane of the [[5-cube]]. A dissection is based on 10 of 30 faces of the [[rhombic triacontahedron]]. The list {{OEIS2C|1=A006245}} defines the number of solutions as 62, with 2 orientations for the first symmetric form, and 10 orientations for the other 6.
{| class=wikitable
|+ Regular decagon dissected into 10 rhombi
|- align=center valign=top
|[[File:5-cube t0.svg|class=skin-invert-image|100px]]<BR>[[5-cube]]
|[[File:Sun_decagon.svg|100px]]
|[[File:Sun2_decagon.svg|100px]]
|[[File:Dart2 decagon.svg|100px]]
|-
|[[File:Halfsun_decagon.svg|100px]]
|[[File:Dart decagon.svg|100px]]
|[[File:Dart decagon ccw.svg|100px]]
|[[File:Cartwheel_decagon.svg|100px]]
|}
{{-}}