View source for Enneagrammic antiprism

{{Infobox polyhedron
|name={9/2} enneagrammic antiprism
|image=Antiprism 9-2.png
|type=[[Uniform polyhedron]]
|faces=2 [[Enneagram (geometry)|{9/2}]]<br>18 [[Triangle|{3}]]
|edges=36
|vertices=18
|wythoff=<nowiki>|2 2 9/2</nowiki>
|schläfli=sr{2,9/2}
|coxeter={{CDD|node_h|2x|node_h|9|rat|2x|node_h}}
|symmetry=''D<sub>9h</sub>'', [2,9],(*299), order 36
|vertex_config=<SUP>9</SUP>/<SUB>2</SUB>.3.3.3
|dual=Enneagrammic deltohedron
|properties=[[Star polyhedron|nonconvex]]
|vertex_figure=Enneagrammic antiprism-2-9 vertfig.png
}}
In [[Geometry|geometry]], an '''enneagrammic antiprism''' is a star antiprism constructed with enneagrammic bases. There are two forms, built on the two enneagrams {9/2} and {9/4}, and one crossed form {9/5}.

A nonuniform 9/7 cross-antiprism can be constructed without equal edge-lengths.

A 9/3 ratio is reducible and so represents a compound polyhedron of 3 triangular antiprisms with 120 degree rotations between them.

== 9/2== 
The first solution is a 9/2 antiprism.
{{Clear}}

== 9/4==
{{Infobox polyhedron
|name={9/4} enneagrammic antiprism
|image=Antiprism 9-4.png
|type=[[Uniform polyhedron]]
|faces=2 [[Enneagram (geometry)|{9/4}]]<br>16 [[Triangle|{3}]]
|edges=36
|vertices=18
|wythoff=<nowiki>|2 2 9/4</nowiki>
|schläfli=sr{2,9/4}
|coxeter={{CDD|node_h|2x|node_h|9|rat|4|node_h}}
|symmetry=''D<sub>9h</sub>'', [2,9],(*299), order 36
|vertex_config=<SUP>9</SUP>/<SUB>4</SUB>.3.3.3
|dual=Enneagrammic deltohedron
|properties=[[Star polyhedron|nonconvex]]
|vertex_figure=Ennegrammic antiprism-4-9 vertfig.png
}}

[[File:Normal Antiprisms 9 4.png|320px]]<BR>9/4-antiprism
{{Clear}}

== 9/5 ==
{{Infobox polyhedron
|name={9/5} enneagrammic crossed-antiprism
|image=Antiprism 9-5.png
|type=[[Uniform polyhedron]]
|faces=2 [[Enneagram (geometry)|{9/5}]]<br>18 [[Triangle|{3}]]
|edges=36
|vertices=18
|wythoff=<nowiki>|2 2 9/5</nowiki>
|schläfli=s{2,18/5}<BR>sr{2,9/5}
|coxeter={{CDD|node_h|2x|node_h|18|rat|5|node}}<BR>{{CDD|node_h|2x|node_h|9|rat|5|node_h}}
|symmetry=''D<sub>9d</sub>'', [2<sup>+</sup>,18], (2*9), order 36
|vertex_config=<SUP>9</SUP>/<SUB>5</SUB>.3.3.3
|dual=Enneagrammic concave deltohedron
|properties=[[Star polyhedron|nonconvex]]
|vertex_figure=Enneagrammic antiprism-5-9 vertfig.png
}}

[[File:Reflex Antiprism 9 4.png|320px]]<BR>9/5-antiprism
{{Clear}}

== See also==
* [[Prismatic uniform polyhedron]]
* Enneagrammic crossed-antiprism

==External links==
*{{MathWorld |urlname=Antiprism |title=Antiprism}}
*[http://www.software3d.com/Prisms.php Paper models of prisms and antiprisms]

{{Polyhedron navigator}}

[[Category:Prismatoid polyhedra]]



{{Sourceattribution|Enneagrammic antiprism|1}}