# 十二面體半形

類別 二十面體半形 {5,3}/2 或 {5,3}5 6 15 10 F=6, E=15, V=10 （χ=1） 5.5.5 A5, 60階 不可定向、 歐拉示性數為1 .mw-parser-output .hlist ul,.mw-parser-output .hlist ol{padding-left:0}.mw-parser-output .hlist li,.mw-parser-output .hlist dd,.mw-parser-output .hlist dt{margin:0;display:inline}.mw-parser-output .hlist dt:after,.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{white-space:normal}.mw-parser-output .hlist dt:after{content:" :"}.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{content:" · ";font-weight:bold}.mw-parser-output .hlist-pipe dd:after,.mw-parser-output .hlist-pipe li:after{content:" | ";font-weight:normal}.mw-parser-output .hlist-hyphen dd:after,.mw-parser-output .hlist-hyphen li:after{content:" - ";font-weight:normal}.mw-parser-output .hlist-comma dd:after,.mw-parser-output .hlist-comma li:after{content:"、";font-weight:normal}.mw-parser-output .hlist dd:last-child:after,.mw-parser-output .hlist dt:last-child:after,.mw-parser-output .hlist li:last-child:after{content:none}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)" ";white-space:nowrap}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)" "}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li:before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child:before,.mw-parser-output .hlist dt ol>li:first-child:before,.mw-parser-output .hlist li ol>li:first-child:before{content:" ("counter(listitem)"\a0 "}.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;display:inline-block}.mw-parser-output .cslist li:after{content:"，"}.mw-parser-output .sslist li:after{content:"；"}.mw-parser-output .cslist li:last-child:after,.mw-parser-output .sslist li:last-child:after{content:none}.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}

## 性質

### 投影

 周界十邊形的投影 周界十二邊形的投影 十二面體半形的另一種投影[3][11]

## 相關多面體

### 皮特里十二面體

類別 以不同顏色表示每個面 皮特里對偶正則地區圖 C6:{3,10}5 {5,3}π{10,3}5[15] 6 30 20 F=6, E=30, V=20 （χ=-4） (不存在) 點群：Ih, H3, [5,3], *532 作為正則地區圖：A5×C2, 120元素[15] 扭歪、正則

 正十二面體的皮特里多邊形 扭歪十邊形 構成皮特里十二面體的扭歪十邊形面

 皮特里十二面體 以正則地區圖表示的皮特里十二面體

## 參考資料

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2. ^ McMullen, Peter; Schulte, Egon, 6C. Projective Regular Polytopes, Abstract Regular Polytopes 1st, Cambridge University Press: 162–165, December 2002, ISBN 0-521-81496-0
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11. ^ Projection of hemidodecahedron. Regular Map database, weddslist.com. [2021-08-01]. （原始内容存档于2021-08-02）.
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13. ^ Balasubramanian, Krishnan. Combinatorics of Petersen graph and its compositions for all irreducible representations for Jahn–Teller, non-rigid molecules and clusters. Journal of Mathematical Chemistry. 2016-08, 54. doi:10.1007/s10910-016-0634-7.
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15. C6:{10,3}5. Regular Map database - map details. [2021-07-30].
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18. ^ C6:{3,10}5. Regular Map database - map details. [2021-07-30].