A trigonal dihedron is a 3-D polyhedron with two triangular faces which share their edges and vertices. In normal Euclidean space, it is degenerate, but can exist as a tiling of the sphere where each face makes up a hemisphere.
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{
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
Regular
t
0
{
3
,
2
}
{\displaystyle t_0 \{3,2\}}
Rectified
t
1
{
3
,
2
}
{\displaystyle t_1 \{3,2\}}
Birectified
t
2
{
3
,
2
}
{\displaystyle t_2 \{3,2\}}
Truncated
t
0
,
1
{
3
,
2
}
{\displaystyle t_{0,1} \{3,2\}}
Bitruncated
t
1
,
2
{
3
,
2
}
{\displaystyle t_{1,2} \{3,2\}}
Cantellated
t
0
,
2
{
3
,
2
}
{\displaystyle t_{0,2} \{3,2\}}
Cantitruncated
t
0
,
1
,
2
{
3
,
2
}
{\displaystyle t_{0,1,2} \{3,2\}}
Trigonal dihedron
Trigonal dihedron
Trigonal hosohedron
Truncated trigonal dihedron
Triangular prism
Triangular prism
Hexagonal prism
{
0
,
2
}
{\displaystyle \{0,2\}}
{
1
,
2
}
{\displaystyle \{1,2\}}
{
2
,
2
}
{\displaystyle \{2,2\}}
{
3
,
2
}
{\displaystyle \{3,2\}}
{
4
,
2
}
{\displaystyle \{4,2\}}
{
5
,
2
}
{\displaystyle \{5,2\}}
{
6
,
2
}
{\displaystyle \{6,2\}}
{
7
,
2
}
{\displaystyle \{7,2\}}
{
8
,
2
}
{\displaystyle \{8,2\}}
...
{
∞
,
2
}
{\displaystyle \{\infty,2\}}
{
π
i
λ
,
2
}
{\displaystyle \{\frac{\pi i}{\lambda},2\}}
Zerogonal dihedron
Monogonal dihedron
Digonal dihedron
Trigonal dihedron
Square dihedron
Pentagonal dihedron
Hexagonal dihedron
Heptagonal dihedron
Octagonal dihedron
...
Apeirogonal dihedron
Pseudogonal dihedron
