Enneagrammic antiprism

{9/2} enneagrammic antiprism
Type	Uniform polyhedron
Faces	2 {9/2} 18 {3}
Edges	36
Vertices	18
Vertex configuration	9/2.3.3.3
Wythoff symbol	|2 2 9/2
Schläfli symbol	sr{2,9/2}
Coxeter diagram
Symmetry group	D9h, [2,9],(*299), order 36
Dual polyhedron	Enneagrammic deltohedron
Properties	nonconvex
Vertex figure

In 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.

9/4

{9/4} enneagrammic antiprism
Type	Uniform polyhedron
Faces	2 {9/4} 16 {3}
Edges	36
Vertices	18
Vertex configuration	9/4.3.3.3
Wythoff symbol	|2 2 9/4
Schläfli symbol	sr{2,9/4}
Coxeter diagram
Symmetry group	D9h, [2,9],(*299), order 36
Dual polyhedron	Enneagrammic deltohedron
Properties	nonconvex
Vertex figure

9/4-antiprism

9/5

{9/5} enneagrammic crossed-antiprism
Type	Uniform polyhedron
Faces	2 {9/5} 18 {3}
Edges	36
Vertices	18
Vertex configuration	9/5.3.3.3
Wythoff symbol	|2 2 9/5
Schläfli symbol	s{2,18/5} sr{2,9/5}
Coxeter diagram
Symmetry group	D9d, [2+,18], (2*9), order 36
Dual polyhedron	Enneagrammic concave deltohedron
Properties	nonconvex
Vertex figure

9/5-antiprism

See also

• Prismatic uniform polyhedron
• Enneagrammic crossed-antiprism

External links

• Weisstein, Eric W.. "Antiprism". http://mathworld.wolfram.com/Antiprism.html. 
• Paper models of prisms and antiprisms