An Apeirogon is a 2-dimensional polygon with a countably infinite number of edges. It can be visualized as a tiling of a one-dimensional line by line segments. In the hyperbolic plane, regular apeirogons are circumscribed by a horocycle, and their lines of symmetry converge to a point at infinity. More general apeirogons include the apeirograms ( for natural ), failed star polygons ( for irrational real ), and pseudogons ( for nonzero imaginary ).
Its Bowers acronym is aze.
Structure and Sections[]

Apeirogon in an order-3 apeirogonal tiling and circumscribed horocycle.
Hypervolumes[]
- vertex count =
- edge length =
- surface area =
Sub-facets[]
- ℵ0 points (0D)
- ℵ0 line segments (1D)
- 1 apeirogon (2D)
See Also[]
- Polytope Wiki. "Apeirogon"
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Zerogon | Monogon | Digon | Triangle | Square | Pentagon | Pentagram | Hexagon | Heptagon | Heptagram | Great heptagram | Octagon | Octagram | Enneagon | Enneagram | Great enneagram | Decagon | Decagram | Hendecagon | Small hendecagram | Hendecagram | Great hendecagram | Grand hendecagram | Dodecagon | Dodecagram | Tridecagon | Small tridecagram | Tridecagram | Medial tridecagram | Great tridecagram | Grand tridecagram | Tetradecagon | Tetradecagram | Great tetradecagram | Pentadecagon | Small pentadecagram | Pentadecagram | Great pentadecagram | Hexadecagon | Small hexadecagram | Hexadecagram | Great hexadecagram | Heptadecagon | Tiny heptadecagram | Small heptadecagram | Heptadecagram | Medial heptadecagram | Great heptadecagram | Giant heptadecagram | Grand heptadecagram | ... | Apeirogon | Failed star polygon (-gon) | Pseudogon (-gon) |
Regular |
Rectified |
Truncated |
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Apeirogon | Apeirogon | Apeirogon |