Uniform Tilings in Hyperbolic Plane - Ideal Triangle Domains

Ideal Triangle Domains

There are infinitely many triangle group families including infinite orders. This article shows uniform tilings in 9 families: (∞ 3 2), (∞ 4 2), (∞ ∞ 2), (∞ 3 3), (∞ 4 3), (∞ 4 4), (∞ ∞ 3), (∞ ∞ 4), and (∞ ∞ ∞).

Read more about this topic:  Uniform Tilings In Hyperbolic Plane

Famous quotes containing the words ideal and/or domains:

    “And into the gulf between cantankerous reality and the male ideal of shaping your world, sail the innocent children. They are right there in front of us—wild, irresponsible symbols of everything else we can’t control.”
    —Hugh O’Neill (20th century)

    “I shall be a benefactor if I conquer some realms from the night, if I report to the gazettes anything transpiring about us at that season worthy of their attention,—if I can show men that there is some beauty awake while they are asleep,—if I add to the domains of poetry.”
    —Henry David Thoreau (1817–1862)