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Statements

Subject Item
dbr:Schläfli_symbol
dbo:wikiPageWikiLink
dbr:Infinite-order_square_tiling
Subject Item
dbr:Infinite-order_square_tiling
rdfs:label
Infinite-order square tiling 無限階正方形鑲嵌
rdfs:comment
In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection. 在幾何學中,無限階正方形鑲嵌是一種位於雙曲平面仿緊空間鑲嵌圖形,由正方形組成,在施萊夫利符號中用{4,∞}來表示,中以表示。每個頂點都是無限多個正方形的公共顶点,也因此使這個圖形無法存於平面上。這個圖形每一條線都可以做為整個圖形的對稱線。 無限階正方形鑲嵌可以視為一系列由正方形組成的多面體之幾何極限,但也可以達到更高階數,利用虛階數表示其階數比無窮大更多,即超無限階正方形鑲嵌,在中以表示。 由於無限階正方形鑲嵌全部都是由正方形組成,每個頂點相同、邊也等長,因此也是一種正幾何圖形。
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Poincaré hyperbolic disk Hyperbolic tiling
dbp:urlname
PoincareHyperbolicDisk HyperbolicTiling
dbo:abstract
In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection. 在幾何學中,無限階正方形鑲嵌是一種位於雙曲平面仿緊空間鑲嵌圖形,由正方形組成,在施萊夫利符號中用{4,∞}來表示,中以表示。每個頂點都是無限多個正方形的公共顶点,也因此使這個圖形無法存於平面上。這個圖形每一條線都可以做為整個圖形的對稱線。 無限階正方形鑲嵌可以視為一系列由正方形組成的多面體之幾何極限,但也可以達到更高階數,利用虛階數表示其階數比無窮大更多,即超無限階正方形鑲嵌,在中以表示。 由於無限階正方形鑲嵌全部都是由正方形組成,每個頂點相同、邊也等長,因此也是一種正幾何圖形。
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