In 2-dimensional hyperbolic geometry , the infinite-order pentagonal tiling is a regular tiling. It has Schläfli symbol of {5,∞}. All vertices are ideal , located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
Symmetry
There is a half symmetry form, , seen with alternating colors:
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n ).
Paracompact uniform apeirogonal/pentagonal tilings
Symmetry: [∞,5], (*∞52)
[∞,5]+ (∞52)
[1+ ,∞,5] (*∞55)
[∞,5+ ] (5*∞)
{∞,5}
t{∞,5}
r{∞,5}
2t{∞,5}=t{5,∞}
2r{∞,5}={5,∞}
rr{∞,5}
tr{∞,5}
sr{∞,5}
h{∞,5}
h2 {∞,5}
s{5,∞}
Uniform duals
V∞5
V5.∞.∞
V5.∞.5.∞
V∞.10.10
V5∞
V4.5.4.∞
V4.10.∞
V3.3.5.3.∞
V(∞.5)5
V3.5.3.5.3.∞
See also
References
External links