Infinite-order apeirogonal tiling on:
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: a or = ∪
Hyperbolic and Spherical Tiling Gallery
* ttp://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch {{Tessellation Apeirogonal tilings Hyperbolic tilings Infinite-order tilings Isogonal tilings Isohedral tilings Regular tilings Self-dual tilings
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, the infinite-order apeirogonal tiling is a regular
The term regular can mean normal or in accordance with rules. It may refer to:
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* Moses Regular (born 1971), America football player
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instrum ...
tiling of the hyperbolic plane. It has Schläfli symbol of , which means it has countably infinitely many apeirogons around all its ideal vertices.
Symmetry
This tiling represents the fundamental domains of *∞∞ symmetry.Uniform colorings
This tiling can also be alternately colored in the ∞,∞,∞)symmetry from 3 generator positions.Related polyhedra and tiling
The union of this tiling and its dual can be seen as orthogonal red and blue lines here, and combined define the lines of a *2∞2∞ fundamental domain. :
: a or = ∪
See also
*Tilings of regular polygons
Euclidean plane tilings by convex regular polygons have been widely used since antiquity. The first systematic mathematical treatment was that of Kepler in his '' Harmonices Mundi'' ( Latin: ''The Harmony of the World'', 1619).
Notation of ...
*List of uniform planar tilings
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings.
There are three regular and eight semiregular tilings in the plane. The semiregular tilings form new tilings from their dua ...
* List of regular polytopes
References
* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations) *External links
* *Hyperbolic and Spherical Tiling Gallery
* ttp://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch {{Tessellation Apeirogonal tilings Hyperbolic tilings Infinite-order tilings Isogonal tilings Isohedral tilings Regular tilings Self-dual tilings