截半 (幾何)

一個截半的立方體(截半立方體)。

幾何學中,截半(英語:Rectification)是一種將多邊形、多面體、密鋪、鑲嵌或更高維的多胞體從每個邊的中點開始切去頂點的一種多面體變換[1],換句話說,就是截角變換的一種特例,即截角截至中點[2]。所得到的多面體將以截面與多面體原本的面為界。考克斯特符號與施萊夫利符號將截半變換記為r,例如r{4,3},而康威記號則將截半變換記為a[3][4],例如aC,r{4,3}與aC皆代表一個截半立方體[5]

康威將截半變換稱為ambo[6]。在圖論演算法中,截半稱為內側圖英语Medial graph

參見

參考文獻

  1. ^ Weisstein, Eric W. (编). Rectification. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. (英语). 
  2. ^ Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 (pp.145-154 Chapter 8: Truncation)
  3. ^ Conway Notation for Polyhedra. www.georgehart.com. [2022-10-15]. (原始内容存档于2014-11-29). 
  4. ^ Weisstein, Eric W. (编). Conway Polyhedron Notation. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. (英语). 
  5. ^ Weisstein, Eric W. (编), Cuboctahedron, (Archimedean solid), at MathWorld--A Wolfram Web Resource,Wolfram Research, Inc. (英语) 
  6. ^ Conway, 2008, p288 table

外部連結

多面體變換
原像 截角 截半 過截角 對偶 擴展英语Expansion (geometry) 全截英语Omnitruncation 交錯
半變換 扭稜
node_1 p node_n1 q node_n2  node_1 p node_1 q node  node p node_1 q node  node p node_1 q node_1  node p node q node_1  node_1 p node q node_1  node_1 p node_1 q node_1  node_h p node q node  node p node_h q node_h  node_h p node_h q node_h 
t0{p,q}
{p,q}
t01{p,q}英语Truncated polyhedron
t{p,q}
t1{p,q}
r{p,q}
t12{p,q}英语Bitruncated polyhedron
2t{p,q}
t2{p,q}
2r{p,q}
t02{p,q}英语Cantellated polyhedron
rr{p,q}
t012{p,q}英语Omnitruncated polyhedron
tr{p,q}
ht0{p,q}
h{q,p}
ht12{p,q}英语Snub polyhedron
s{q,p}
ht012{p,q}英语Snub polyhedron
sr{p,q}

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