A pseudogonal hosohedron is a regular hyperbolic tiling constructed similarly to the apeirogonal hosohedron . It is composed of infinitely many digonal faces that share their vertices and its vertex figure is some pseudogon . Its vertices are ultraideal points, meaning that they do not exist in the plane nor are ideal points.
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{
2
,
0
}
{\displaystyle \{2,0\}}
{
2
,
1
}
{\displaystyle \{2,1\}}
{
2
,
2
}
{\displaystyle \{2,2\}}
{
2
,
3
}
{\displaystyle \{2,3\}}
{
2
,
4
}
{\displaystyle \{2,4\}}
{
2
,
5
}
{\displaystyle \{2,5\}}
{
2
,
6
}
{\displaystyle \{2,6\}}
{
2
,
7
}
{\displaystyle \{2,7\}}
{
2
,
8
}
{\displaystyle \{2,8\}}
...
{
2
,
∞
}
{\displaystyle \{2,\infty\}}
{
2
,
π
i
λ
}
{\displaystyle \{2,\frac{\pi i}{\lambda}\}}
Zerogonal hosohedron
Monogonal hosohedron
Digonal dihedron
Trigonal hosohedron
Square hosohedron
Pentagonal hosohedron
Hexagonal hosohedron
Heptagonal hosohedron
Octagonal hosohedron
...
Apeirogonal hosohedron
Pseudogonal hosohedron
{
2
,
π
i
λ
}
{\displaystyle \{2,\frac{\pi i}{\lambda}\}}
{
3
,
π
i
λ
}
{\displaystyle \{3,\frac{\pi i}{\lambda}\}}
{
4
,
π
i
λ
}
{\displaystyle \{4, \frac{\pi i}{\lambda}\}}
{
5
,
π
i
λ
}
{\displaystyle \{5,\frac{\pi i}{\lambda}\}}
{
6
,
π
i
λ
}
{\displaystyle \{6,\frac{\pi i}{\lambda}\}}
{
7
,
π
i
λ
}
{\displaystyle \{7,\frac{\pi i}{\lambda}\}}
{
8
,
π
i
λ
}
{\displaystyle \{8,\frac{\pi i}{\lambda}\}}
...
{
∞
,
π
i
λ
}
{\displaystyle \{\infty,\frac{\pi i}{\lambda}\}}
{
π
i
λ
1
,
π
i
λ
2
}
{\displaystyle \{\frac{\pi i}{\lambda_1},\frac{\pi i}{\lambda_2}\}}
Pseudogonal hosohedron
Imaginary-order triangular tiling
Imaginary-order square tiling
Imaginary-order pentagonal tiling
Imaginary-order hexagonal tiling
Imaginary-order heptagonal tiling
Imaginary-order octagonal tiling
...
Imaginary-order apeirogonal tiling
Imaginary-order pseudogonal tiling
