1 . 半正多面体亦称“阿基米德多面体”,是由边数不全相同的正多边形围成的多面体,体现了数学的对称美.二十四等边体就是一种半正多面体,它是由正方体的各条棱的中点连接形成的几何体、它由八个正三角形和六个正方形围成(如图所示),若它所有棱的长都为2,则下列说法错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/194b061c-3a15-4dec-99e7-60f59e8c0187.png?resizew=148)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/194b061c-3a15-4dec-99e7-60f59e8c0187.png?resizew=148)
A.该二十四等边体的表面积为![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.该半正多面体的顶点数V、面数F、棱数E,满足关系式![]() |
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2019高三·全国·专题练习
2 . 我国古代数学名著《九章算术》中记载:“今有羡除”.刘徽注:“羡除,隧道也.其所穿地,上平下邪.”小明仿制羡除裁剪出如图所示的纸片,在等腰梯形
中,
,
,在等腰梯形
中,
,
.将等腰梯形
沿
折起,使
,则五面体
中异面直线
与
所成角的余弦值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/cbf4cd57-f371-43ac-a3f9-3cd14d2723e4.png?resizew=290)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/cbf4cd57-f371-43ac-a3f9-3cd14d2723e4.png?resizew=290)
A.![]() | B.![]() | C.![]() | D.![]() |
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