A pentagonal hosohedron is a 3-D polyhedron with five digonal faces. In normal Euclidean space, it is degenerate, but can exist as a tiling of the sphere.
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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
Regular
t
0
{
5
,
2
}
{\displaystyle t_0 \{5,2\}}
Rectified
t
1
{
5
,
2
}
{\displaystyle t_1 \{5,2\}}
Birectified
t
2
{
5
,
2
}
{\displaystyle t_2 \{5,2\}}
Truncated
t
0
,
1
{
5
,
2
}
{\displaystyle t_{0,1} \{5,2\}}
Bitruncated
t
1
,
2
{
5
,
2
}
{\displaystyle t_{1,2} \{5,2\}}
Cantellated
t
0
,
2
{
5
,
2
}
{\displaystyle t_{0,2} \{5,2\}}
Cantitruncated
t
0
,
1
,
2
{
5
,
2
}
{\displaystyle t_{0,1,2} \{5,2\}}
Pentagonal dihedron
Pentagonal dihedron
Pentagonal hosohedron
Truncated pentagonal dihedron
Pentagonal prism
Pentagonal prism
Decagonal prism
{
2
,
5
}
{\displaystyle \{2,5\}}
{
3
,
5
}
{\displaystyle \{3, 5\}}
{
4
,
5
}
{\displaystyle \{4,5\}}
{
5
,
5
}
{\displaystyle \{5,5\}}
{
6
,
5
}
{\displaystyle \{6,5\}}
{
7
,
5
}
{\displaystyle \{7,5\}}
{
8
,
5
}
{\displaystyle \{8,5\}}
...
{
∞
,
5
}
{\displaystyle \{\infty,5\}}
{
π
i
λ
,
5
}
{\displaystyle \{\frac{\pi i}{\lambda},5\}}
Pentagonal hosohedron
Icosahedron
Order-5 square tiling
Order-5 pentagonal tiling
Order-5 hexagonal tiling
Order-5 heptagonal tiling
Order-5 octagonal tiling
...
Order-5 apeirogonal tiling
Order-5 pseudogonal tiling
