An imaginary-order triangular tiling is a regular noncompact hyperbolic tiling with triangular faces and pseudogonal vertex figures .
The vertices of any given imaginary-order triangular tiling are considered ultraideal points, which means that they are not in the plane nor are ideal points. The dual of an imaginary-order triangular tiling is an order-3 pseudogonal tiling .
Gallery [ ]
{
3
,
11
i
}
{\displaystyle \{3, 11i\}}
{
3
,
10
i
}
{\displaystyle \{3, 10i\}}
{
3
,
9
i
}
{\displaystyle \{3, 9i\}}
{
3
,
8
i
}
{\displaystyle \{3, 8i\}}
{
3
,
7
i
}
{\displaystyle \{3, 7i\}}
{
3
,
6
i
}
{\displaystyle \{3, 6i\}}
{
3
,
5
i
}
{\displaystyle \{3, 5i\}}
{
3
,
4
i
}
{\displaystyle \{3, 4i\}}
{
3
,
3
i
}
{\displaystyle \{3, 3i\}}
{
3
,
2
i
}
{\displaystyle \{3, 2i\}}
{
3
,
i
}
{\displaystyle \{3, i\}}
See Also [ ]
{
3
,
2
}
{\displaystyle \{3,2\}}
{
3
,
3
}
{\displaystyle \{3, 3\}}
{
3
,
4
}
{\displaystyle \{3, 4\}}
{
3
,
5
}
{\displaystyle \{3, 5\}}
{
3
,
6
}
{\displaystyle \{3,6\}}
{
3
,
7
}
{\displaystyle \{3,7\}}
{
3
,
8
}
{\displaystyle \{3,8\}}
...
{
3
,
∞
}
{\displaystyle \{3,\infty\}}
{
3
,
π
i
λ
}
{\displaystyle \{3,\frac{\pi i}{\lambda}\}}
Trigonal dihedron
Tetrahedron
Octahedron
Icosahedron
Triangular tiling
Order-7 triangular tiling
Order-8 triangular tiling
...
Infinite-order triangular tiling
Imaginary-order triangular tiling
{
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
Regular
t
0
{
π
i
λ
,
3
}
{\displaystyle t_0 \{\frac{\pi i}{\lambda},3\}}
Rectified
t
1
{
π
i
λ
,
3
}
{\displaystyle t_1 \{\frac{\pi i}{\lambda},3\}}
Birectified
t
2
{
π
i
λ
,
3
}
{\displaystyle t_2 \{\frac{\pi i}{\lambda},3\}}
Truncated
t
0
,
1
{
π
i
λ
,
3
}
{\displaystyle t_{0,1} \{\frac{\pi i}{\lambda},3\}}
Bitruncated
t
1
,
2
{
π
i
λ
,
3
}
{\displaystyle t_{1,2} \{\frac{\pi i}{\lambda},3\}}
Cantellated
t
0
,
2
{
π
i
λ
,
3
}
{\displaystyle t_{0,2} \{\frac{\pi i}{\lambda},3\}}
Cantitruncated
t
0
,
1
,
2
{
π
i
λ
,
3
}
{\displaystyle t_{0,1,2} \{\frac{\pi i}{\lambda},3\}}
Order-3 pseudogonal tiling
Tripseudogonal tiling
Imaginary-order triangular tiling
Truncated order-3 pseudogonal tiling
Truncated imaginary-order triangular tiling
Rhombitripseudogonal tiling
Truncated tripseudogonal tiling