Uniform apeirogonal antiprism  

Type  Semiregular tiling 
Vertex configuration  3.3.3.∞ 
Schläfli symbol  sr{2,∞} or 
Wythoff symbol   2 2 ∞ 
Coxeter diagram  
Symmetry  [∞,2^{+}], (∞22) 
Rotation symmetry  [∞,2]^{+}, (∞22) 
Bowers acronym  Azap 
Dual  Apeirogonal deltohedron 
Properties  Vertextransitive 
In geometry, an apeirogonal antiprism or infinite antiprism^{[1]} is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane.
If the sides are equilateral triangles, it is a uniform tiling. In general, it can have two sets of alternating congruent isosceles triangles, surrounded by two halfplanes.
The apeirogonal antiprism is the arithmetic limit of the family of antiprisms sr{2, p} or p.3.3.3, as p tends to infinity, thereby turning the antiprism into a Euclidean tiling.
Similarly to the uniform polyhedra and the uniform tilings, eight uniform tilings may be based from the regular apeirogonal tiling. The rectified and cantellated forms are duplicated, and as two times infinity is also infinity, the truncated and omnitruncated forms are also duplicated, therefore reducing the number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism.
(∞ 2 2)  Wythoff symbol 
Schläfli symbol 
Coxeter diagram 
Vertex config. 
Tiling image  Tiling name 

Parent  2  ∞ 2  {∞,2}  ∞.∞  Apeirogonal dihedron  
Truncated  2 2  ∞  t{∞,2}  2.∞.∞  
Rectified  2  ∞ 2  r{∞,2}  2.∞.2.∞  
Birectified (dual) 
∞  2 2  {2,∞}  2^{∞}  Apeirogonal hosohedron  
Bitruncated  2 ∞  2  t{2,∞}  4.4.∞  Apeirogonal prism  
Cantellated  ∞ 2  2  rr{∞,2}  
Omnitruncated (Cantitruncated) 
∞ 2 2   tr{∞,2}  4.4.∞  
Snub   ∞ 2 2  sr{∞,2}  3.3.3.∞  Apeirogonal antiprism
Notes
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Referencesedit
