在幾何學中,正方形鑲嵌又稱正方形密鋪,亦稱為方形網格,是一種正多邊形在平面上的密鋪,又稱正鑲嵌圖。
Quick Facts 類別, 對偶多面體 ...
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其在施萊夫利符號中,用{4,4}來表示,這意味著每個頂點周圍都有四個正方形。
康威將之稱為quadrille。
正方形的內角是為90度,四個正方形拼接,以便填滿一個完整的360度。這是三個的平面正鑲嵌圖之一。另外兩個是正三角形鑲嵌和正六邊形鑲嵌。
正方形鑲嵌共有9種不同的半正塗色,其中5種是有著考克斯特符號的鏡面構造。這些半正的表面塗色可以由四個正方形為單位構成的單元構成:
More information 符號, 圖像 ...
符號
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1111
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1112
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1122
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1123
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圖像
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符號
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1212
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1213
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1234
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圖像
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這裡用頂點周圍的四個正方形來標記不同的塗色:1111、1112(i)、1112(ii)、1122、1123(i)、1123(ii)、1212、1213、1234。(i)有著簡單的鏡面對稱,(ii)有著錯位的鏡面對稱。)
More information 1112(i), 1112(ii) ...
1111 |
1212 |
1213 |
1122 |
1234
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png)
![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_h1](//upload.wikimedia.org/wikipedia/commons/4/48/CDel_node_h1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_h1](//upload.wikimedia.org/wikipedia/commons/4/48/CDel_node_h1.png)
![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png)
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![node_h0](//upload.wikimedia.org/wikipedia/commons/5/5d/CDel_node_h0.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_h0](//upload.wikimedia.org/wikipedia/commons/5/5d/CDel_node_h0.png)
![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![2](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![infin](//upload.wikimedia.org/wikipedia/commons/b/be/CDel_infin.png)
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p4m [4,4] (*442)
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pmm [1+,4,4,1+] = [∞,2,∞] (*2222)
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1112(i) |
1112(ii) |
1123(ii) |
1123(i)
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p4m [4,4] (*442)
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c2 [∞,2+,∞] (2*22)
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pmm [∞,2,∞] (*2222)
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More information 對稱性: [4,4], (*442), [4,4]+, (442) ...
正方形鑲嵌家族的半正鑲嵌
對稱性: [4,4], (*442)
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[4,4]+, (442)
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[4,4+], (4*2)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_1](//upload.wikimedia.org/wikipedia/commons/b/bd/CDel_node_1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_h](//upload.wikimedia.org/wikipedia/commons/2/28/CDel_node_h.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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t0{4,4}
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t0,1{4,4}
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t1{4,4}
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t1,2{4,4}
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t2{4,4}
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t0,2{4,4}
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t0,1,2{4,4}
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s{4,4}
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h0,1{4,4}
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半正對偶
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_f1](//upload.wikimedia.org/wikipedia/commons/9/9b/CDel_node_f1.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node_fh](//upload.wikimedia.org/wikipedia/commons/6/6f/CDel_node_fh.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_fh](//upload.wikimedia.org/wikipedia/commons/6/6f/CDel_node_fh.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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![node](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png) ![node_fh](//upload.wikimedia.org/wikipedia/commons/6/6f/CDel_node_fh.png) ![4](//upload.wikimedia.org/wikipedia/commons/8/8c/CDel_4.png)
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V4.4.4.4
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V4.8.8
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V4.4.4.4
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V4.8.8
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V4.4.4.4
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V4.4.4.4
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V4.8.8
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V3.3.4.3.4
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Coxeter, Complex Regular polytopes,[1] p.141
- Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p. 296, Table II: Regular honeycombs
- Klitzing, Richard. 2D Euclidean tilings o4o4x - squat - O1. bendwavy.org.
- Williams, Robert. The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. 1979. ISBN 0-486-23729-X. p36
- Grünbaum, Branko ; and Shephard, G. C. Tilings and Patterns. New York: W. H. Freeman. 1987. ISBN 0-7167-1193-1. (Chapter 2.1: Regular and uniform tilings, p. 58-65)
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1]
- 埃里克·韋斯坦因. Square Grid. MathWorld.
- 埃里克·韋斯坦因. Regular tessellation. MathWorld.
- 埃里克·韋斯坦因. Uniform tessellation. MathWorld.