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阿基米德立體

阿基米德立體是一種高度對稱的半正多面體,且使用兩種或以上的正多邊形為面的凸多面體(不包括棱柱反棱柱),並且都是可以從正多面體經過截角、截半、截邊等操作構造。阿基米德立體的每個頂點的情況相同,共有13種。阿基米德曾研究半正多面體(雖然其研究紀錄已佚),故有人將半正多面體喚作阿基米德立體。因為面是由正多邊形組成的,每個相鄰的正多邊形的邊長相等,故阿基米德立體的邊均有相同長度。阿基米德立體对偶多面体卡塔蘭立體

半正多面體一詞不只是指13種阿基米德立體,而是指所有具有對稱群且由2種或2種以上正多邊形所組成的多面體[1][2]

截半多面體(阿基米德立體)

柏拉圖立體中,從一條棱斬去另一條棱的中點所得出的多面體。这两种多面体又合称为拟正多面体

名稱
(頂點佈局)
透視圖 旋轉透視圖 立體圖 展開圖 頂點 所屬點群
截半立方體
(截半八面體)
(3.4.3.4)
Cuboctahedron Cuboctahedron  14  三角形×8
正方形×6
24 12 Oh
截半二十面體
(截半十二面體)
(三十二面體)
(3.5.3.5)
Icosidodecahedron Icosidodecahedron 32 三角形×20
五邊形×12
60 30 Ih

截角多面體

名稱
(頂點佈局)
透視圖 旋轉透視圖 立體圖 展開圖 頂點 所屬點群
截角四面體
(3.6.6)
Truncated tetrahedron Truncated tetrahedron 8 三角形×4
六邊形×4
18 12 Td
截角立方體
(3.8.8)
Truncated hexahedron Truncated hexahedron 14 三角形×8
八邊形×6
36 24 Oh
截角八面體
(4.6.6)
Truncated octahedron Truncated octahedron 14 正方形×6
六邊形×8
36 24 Oh
小斜方截半立方體
(3.4.4.4 )
Rhombicuboctahedron Rhombicuboctahedron 26 三角形×8
正方形×18
48 24 Oh
大斜方截半立方體
(4.6.8)
Truncated cuboctahedron Truncated cuboctahedron 26 正方形×12
六邊形×8
八邊形×6
72 48 Oh
扭稜立方體
(3.3.3.3.4)
(具有兩種手性鏡像)
Snub hexahedron (Ccw)
Snub hexahedron (Cw)
Snub hexahedron (Ccw)
Snub hexahedron (Cw)
38 三角形×32
正方形×6
60 24 O群
截角十二面體
(3.10.10)
Truncated dodecahedron Truncated dodecahedron 32 三角形×20
十邊形×12
90 60 Ih
截角二十面體(足球的形狀)
(5.6.6)
Truncated icosahedron Truncated icosahedron 32 五邊形×12
六邊形×20
90 60 Ih
小斜方截半二十面體
(小斜方三十二面體)
(3.4.5.4)
Rhombicosidodecahedron Rhombicosidodecahedron 62 三角形×20
正方形×30
五邊形×12
120 60 Ih
大斜方截半二十面體
(大截角截半二十面體)
(大斜方三十二面體)
(大截角三十二面體)
(4.6.10)
Truncated icosidodecahedron Truncated icosidodecahedron 62 正方形×30
六邊形×20
十邊形×12
180 120 Ih
扭稜十二面體
(3.3.3.3.5)
(具有兩種手性鏡像)
Snub dodecahedron (Ccw)
Snub dodecahedron (Cw)
Snub dodecahedron (Ccw)
Snub dodecahedron (Cw)
92 三角形×80
五邊形×12
150 60 I群

參考文獻

  1. ^ 《圖解數學辭典》天下遠見出版 ISBN 986-417-614-5
  2. ^ Illustrated Dictionary of Maths 2003 Usborne Publishing Ltd.
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