Top Qs
Timeline
Chat
Perspective

Uniform tiling symmetry mutations

From Wikipedia, the free encyclopedia

Uniform tiling symmetry mutations
Remove ads
Remove ads

In geometry, a symmetry mutation is a mapping of fundamental domains between two symmetry groups.[1] They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean tilings to hyperbolic tilings. Hyperbolic tilings can also be divided between compact, paracompact and divergent cases.

More information Spherical tilings (n = 3..5), Euclidean plane tiling (n = 6) ...

The uniform tilings are the simplest application of these mutations, although more complex patterns can be expressed within a fundamental domain.

This article expressed progressive sequences of uniform tilings within symmetry families.

Remove ads

Mutations of orbifolds

Orbifolds with the same structure can be mutated between different symmetry classes, including across curvature domains from spherical, to Euclidean to hyperbolic. This table shows mutation classes.[1] This table is not complete for possible hyperbolic orbifolds.

More information Orbifold, Spherical ...
Remove ads

*n22 symmetry

Regular tilings

More information Space, Spherical ...
More information Space, Spherical ...

Prism tilings

More information Space, Spherical ...

Antiprism tilings

More information Space, Spherical ...
Remove ads

*n32 symmetry

Regular tilings

More information Spherical, Euclid. ...
More information Spherical, Euclidean ...

Truncated tilings

More information Symmetry*n32 [n,3], Spherical ...
More information Sym.*n42 [n,3], Spherical ...

Quasiregular tilings

More information Sym.*n32 [n,3], Spherical ...
More information Symmetry mutations of dual quasiregular tilings: V(3.n)2, *n32 ...

Expanded tilings

More information Symmetry*n32 [n,3], Spherical ...
More information Symmetry*n32 [n,3], Spherical ...

Omnitruncated tilings

More information Sym.*n32 [n,3], Spherical ...

Snub tilings

More information Symmetry n32, Spherical ...
Remove ads

*n42 symmetry

Regular tilings

More information Spherical, Euclidean ...
More information Spherical, Euclidean ...

Quasiregular tilings

More information Symmetry*4n2 [n,4], Spherical ...
More information *n42 symmetry mutations of quasiregular dual tilings: V(4.n)2, Symmetry*4n2 [n,4] ...

Truncated tilings

More information Symmetry*n42 [n,4], Spherical ...
More information Symmetry*n42 [n,4], Spherical ...

Expanded tilings

More information Symmetry [n,4], (*n42), Spherical ...

Omnitruncated tilings

More information Symmetry*n42 [n,4], Spherical ...

Snub tilings

More information Symmetry 4n2, Spherical ...
Remove ads

*n52 symmetry

Regular tilings

More information Sphere, Hyperbolic plane ...

*n62 symmetry

Regular tilings

More information Spherical, Euclidean ...

*n82 symmetry

Regular tilings

More information Space, Spherical ...

References

Loading content...

Sources

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads