View source for Petrial great stellated dodecahedron

{{Infobox polytope
|img=Petrial great stellated dodecahedron.gif
|faces=6 [[skew decagram]]s
|euler=-4
|edges=30
|vertices=20
|verf=[[Triangle]]
|schläfli=<math>\{5/2,3\}^\pi</math><br> <math>\{10/3,3\}_{5/2}</math><ref>{{harvcoltxt|McMullen|Schulte|1997|p=460}}</ref>
|stype={{Schlink|10|3}}
|space=Spherical
|type=[[Regular polytope|Regular]]
|rank=3
|hull=[[Dodecahedron]]
|army=[[Doe]]
|regiment=[[Great stellated dodecahedron|Gissid]]
|petrial=[[Great stellated dodecahedron]]
|conjugate=[[Petrial dodecahedron]]
|flags=120
|convex=No
|orient=No
|genus=6
}}
The '''petrial great stellated dodecahedron''' is a [[regular]] [[skew]] [[polyhedron]] and is the [[Petrie dual]] of the [[great stellated dodecahedron]], and so it shares both of its vertices and edges with the great stellated dodecahedron. It consists of 6 [[skew decagram]]s and has an [[Euler characteristic]] of -4.

==Vertex coordinates==
The vertices of the petrial great stellated dodecahedron are identical to those of the [[great stellated dodecahedron]], which is the regiment colonel.
==Related polyhedra==
The [[rectification]] of the petrial great stellated dodecahedron is the  [[great icosihemidodecahedron]], which is uniform.

==External links==
* {{Wikipedia|Petrie dual}}
* {{atlas|120/35/13|{10,3}*120b}}

==References==
{{reflist}}

==Bibliography==
* {{ cite journal
  | last1 =
    McMullen
  | first1 =
    Peter
  | first2 =
    Egon
  | last2 =
    Schulte
  | title =
    Regular Polytopes in Ordinary Space
  | journal =
    Discrete Computational Geometry
  | issue =
    47
  | pages =
    449-478
  | doi =
    10.1007/PL00009304
  | date =
    1997
  | url =
    https://link.springer.com/content/pdf/10.1007/PL00009304.pdf
  }}

{{Regular polyhedron}}

[[Category:Gissid regiment]]
[[Category:Regular skew polyhedra in 3-dimensions]]
[[Category:Regular pure polyhedra]]
[[Category:H3 symmetry]]
[[Category:Schläfli type 10,3]]
[[Category:Polyhedra with 6 faces]]