# 截角十二面体

(按這裡觀看旋轉模型)

verse-and-dimensions的wikiaBowers acronym
tid

2 3 | 5

32
90

20個{3}
12個{10}

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 3.10.10（頂點圖） 三角化二十面體（對偶多面體） （展開圖）

## 性質

### 體積與表面積

${\displaystyle A=5\left({\sqrt {3}}+6{\sqrt {5+2{\sqrt {5}}}}\right)a^{2}\approx 100.990\,76a^{2}}$
${\displaystyle V={\frac {5}{12}}\left(99+47{\sqrt {5}}\right)a^{3}\approx 85.039\,6646a^{3}}$

### 頂點坐標

${\displaystyle \left(0\,,\pm {\frac {1}{\varphi }}\,,\pm {\left({\begin{smallmatrix}2+\varphi \end{smallmatrix}}\right)}\right)}$
${\displaystyle \left(\pm {\frac {1}{\varphi }}\,,\pm {\varphi }\,,\pm {2{\varphi }}\right)}$
(±φ, ±2, ±(φ + 1))

## 頂點佈局

 截角十二面體（原像） 大雙三角十二面截半二十面體

## 相關多面體及密鋪

{5,3} t0,1{5,3} t1{5,3} t0,1{3,5} {3,5} t0,2{5,3} t0,1,2{5,3} s{5,3}

V5.5.5 V3.10.10 V3.5.3.5 V5.6.6 V3.3.3.3.3 V3.4.5.4 V4.6.10 V3.3.3.3.5

## 參考文獻

1. Williams, Robert. The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. 1979. ISBN 0-486-23729-X. (Section 3-9)
2. Cromwell, P. Polyhedra. United Kingdom: Cambridge. 1997: 79-86 Archimedean solids. ISBN 0-521-55432-2.
1. ^ Weisstein, Eric W. (编). Truncated Dodecahedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
2. ^ Cromwell, P. Polyhedra, CUP hbk (1997), pbk. (1999). Ch.2 p.79-86 Archimedean solids
3. ^ Kasahara, K. "The Final Semiregular Polyhedron". Origami Omnibus: Paper-Folding for Everyone.. Tokyo: Japan Publications. 1988: p. 229. ISBN 978-4817090010.
4. ^ Geometry Technologies. "Truncated Dodecahedron.". scienceu. [2016-08-30]. （原始内容存档于2016-08-06）.
5. ^ Cundy, H. and Rollett, A. "Truncated Dodecahedron. 3.102." §3.7.9 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 109, 1989. ISBN 978-0906212202
6. ^ Weisstein, Eric W. (编). Icosahedral group. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
7. ^ Archimedean Solids: Truncated Dodecahedron. dmccooey.com. （原始内容存档于2016-03-12）.
8. ^ Weisstein, Eric W. (编). 大二十合二十合十二體. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
9. ^ Weisstein, Eric W. (编). 大二重三角十二面截半二十面體. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
10. ^ Weisstein, Eric W. (编). 大十二合二十面體. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
11. ^ : The Theory of Uniform Polytopes and Honeycombs, Ph.D. Dissertation, University of Toronto, 1966