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square tiling honeycomb : ウィキペディア英語版
square tiling honeycomb

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|bgcolor=#e7dcc3|Coxeter diagrams||



|-
|bgcolor=#e7dcc3|Cells|| 40px 40px 40px
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|bgcolor=#e7dcc3|Faces||Square
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|bgcolor=#e7dcc3|Edge figure||Triangle
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|bgcolor=#e7dcc3|Vertex figure||80px
cube,
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|bgcolor=#e7dcc3|Dual||Order-4 octahedral honeycomb
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|bgcolor=#e7dcc3|Coxeter groups||()
() ↔ ()
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|bgcolor=#e7dcc3|Properties||Regular
|}
In the geometry of hyperbolic 3-space, the square tiling honeycomb, is one of 11 paracompact regular honeycombs. It is called ''paracompact'' because it has infinite cells, whose vertices exist on horospheres and converge to a single ideal point at infinity. Given by Schläfli symbol , has three square tilings, around each edge, and 6 square tilings around each vertex in an cubic vertex figure.〔Coxeter ''The Beauty of Geometry'', 1999, Chapter 10, Table III〕
== Rectified order-4 square tiling ==
It is also seen as a rectified order-4 square tiling honeycomb, r:
=
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!|| =
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|240px||240px
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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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