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=== Dissections=== [[Coxeter]] states that every [[zonogon]] (a 2''m''-gon whose opposite sides are parallel and of equal length) can be dissected into <math>\tbinom{m}{2}</math> or {{nowrap|{{sfrac|1|2}}''m''(''m'' β 1)}} parallelograms. These tilings are contained as subsets of vertices, edges and faces in orthogonal projections [[Hypercube|''m''-cubes]].<ref>[[Coxeter]], Mathematical recreations and Essays, Thirteenth edition, p.141</ref> In particular, this is true for any regular polygon with an even number of sides, in which case the parallelograms are all rhombi. The list {{OEIS2C|1=A006245}} gives the number of solutions for smaller polygons. {| class="wikitable skin-invert-image" |+ Example dissections for select even-sided regular polygons ! |[[File:6-gon rhombic dissection.svg |100px]] |[[File:8-gon rhombic dissection.svg |100px]] |[[File:Sun_decagon.svg |100px]] |[[File:12-gon rhombic dissection.svg |100px]] |[[File:14-gon-dissection-star.svg |100px]] |[[File:16-gon rhombic dissection.svg |100px]] |- align=center valign=top !scope=row style="text-align:left" |Sides |[[Hexagon#Dissection|6]] |[[Octagon#Dissection|8]] |[[Decagon#Dissection|10]] |[[Dodecagon#Dissection|12]] |[[Tetradecagon#Dissection|14]] |[[Hexadecagon#Dissection|16]] |- align=center valign=top !scope=row style="text-align:left" |Rhombs |3 |6 |10 |15 |21 |28 |- |} {| class="wikitable skin-invert-image" ! |[[File:18-gon-dissection-star.svg |100px]] |[[File:20-gon rhombic dissection.svg |100px]] |[[File:24-gon rhombic dissection.svg |100px]] |[[File:30-gon-dissection-star.svg |100px]] |[[File:40-gon rhombic dissection.svg |100px]] |[[File:50-gon-dissection-star.svg |100px]] |- align=center valign=top !scope=row style="text-align:left" |Sides |[[Octadecagon#Dissection|18]] |[[Icosagon#Dissection|20]] |[[Icositetragon#Dissection|24]] |[[Triacontagon#Dissection|30]] |40 |50 |- align=center valign=top !scope=row style="text-align:left" |Rhombs |36 |45 |66 |105 |190 |300 |}
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