Editing Star polygon (section)

===Examples in tilings===
{{See|Uniform tiling#Uniform tilings using star polygons as concave alternating faces}}
These polygons are often seen in tiling patterns. The parametric angle 𝛼 (in degrees or radians) can be chosen to match [[internal angle]]s of neighboring polygons in a tessellation pattern. In his 1619 work ''[[Harmonice Mundi]]'', among periodic tilings, [[Johannes Kepler]] includes nonperiodic tilings, like that with three regular pentagons and one regular star pentagon fitting around certain vertices, 5.5.5.5/2, and related to modern [[Penrose tiling]]s.<ref name="maa.org">[https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf Branko Grunbaum and Geoffrey C. Shephard, Tilings by Regular Polygons, Mathematics Magazine #50 (1977), pp. 227–247, and #51 (1978), pp. 205–206]</ref>
{| class="wikitable nowrap"
|+ Examples of isogonal tilings with isotoxal simple stars<ref>[http://www.polyomino.org.uk/publications/2004/star-polygon-tiling.pdf Tiling with Regular Star Polygons], Joseph Myers</ref>
!valign=center|Isotoxal simple<BR>''n''-pointed stars
!"Triangular" stars<BR>(''n'' = 3)
!"Square" stars<BR>(''n'' = 4)
!colspan=3|"Hexagonal" stars<BR>(''n'' = 6)
!"Octagonal" stars<BR>(''n'' = 8)
|- align=center valign=center
!Image of tiling
|[[File:Triangle and triangular star tiling.svg|140px]]
|[[File:Octagon star square tiling.svg|150px]]
|[[File:Hexagon hexagram tiling.png|140px]]
|[[File:Gyrated truncated hexagonal tiling2.png|140px]]
|[[File:Trihexagonal tiling stars.svg|150px]]
|[[File:Hexagon hexagram tiling2.png|140px]]
|- align=center valign=center
!Vertex config.
|3.3{{supsub|*|𝛼}}.3.3{{supsub|**|𝛼}}
|8.4{{supsub|*|π/4}}.8.4{{supsub|*|π/4}}
|6.6{{supsub|*|π/3}}.6.6{{supsub|*|π/3}}
|3.6{{supsub|*|π/3}}.6{{supsub|**|π/3}}
|3.6.6{{supsub|*|π/3}}.6
|not edge-to-edge
|}