Section outline

  • Polyhedra
    ::聚六极

    A polyhedron (plural polyhedra) is a closed geometric shape made entirely of polygonal side s.  Prisms (introduced in the lesson  ) are an example of polyhedra.
    ::多面形(多元多面形)是完全由多边形面组成的封闭式几何形状。棱柱(在课程中引入)是多面形的一个例子。

    Use the interactive below to build polyhedra using squares and triangles. Observe how many of each shape you use and what shape each of the faces are.
    ::使用下面的交互效果来使用方形和三角形构建 聚赫德拉 。 观察您使用的每个形状的大小, 以及每个脸部的形状 。

     

    INTERACTIVE
    Build Polyhedra
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    • Click on the appropriate shapes on the bottom and then the corresponding faces on the polyhedron to place the shape there.
      ::单击底部的适当形状,然后单击聚希德龙的对应面孔,将形状放在那里。
    • Drag the screen to rotate the polyhedron.
      ::拖曳屏幕以旋转多面体 。
    • Once finished, moved the slider to look at previous polyhedra.
      ::完成后, 移动滑动器查看上一个 monhedra 。
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    Nets
    ::净额净额净额

    In the opening activity,  you created polyhedra from 2-dimensional shapes . This idea is  important for understanding what a net is . A net is a 2-dimensional pattern that can be folded into a 3-dimensional solid.
    ::在开场活动中,您从二维形状中创建了多面体。 这个想法对于了解网是什么很重要。 网是一个二维模式, 可以折叠成三维固态 。

    In this next interactive, you will observe the nets of polyhedra and the shapes of the faces that make up each net.
    ::在下一场互动中,你们将观察聚赫德拉的网状和构成每个网的面孔的形状。

     

    INTERACTIVE
    Nets
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    • Choose one of the polyhedra from the dropdown menu.
      ::从下拉菜单中选择一个 monhedra 。
    • Click the buttons to fold and unfold the net.
      ::单击按钮折叠并展开网。
    • Drag the screen to change your point of view. Use two fingers on your trackpad or touch screen or scroll the mouse wheel to zoom.
      ::拖曳屏幕以改变您的视图点。 在您的跟踪板上使用两根手指或触摸屏幕或滚动鼠标方向盘以缩放 。
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    1.

    The net of a tetrahedron has triangles and squares.
    ::四面线网已输入您的答三角形并输入您的答方方形。

     

     

    Matching Polyhedra With Their Nets
    ::匹配多面体及其网网

    Through this interactive, you will match polyhedra and their nets by observing how they would fold and unfold.
    ::通过这段互动,你将会通过观察它们如何折叠和展出 来匹配聚赫德拉和它们的网。

     

    INTERACTIVE
    Matching Polyhedra with Their Nets
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    • Use the arrow buttons at the bottom to find the net that matches the polyhedron.

      ::使用底部的箭头按钮找到与多面体匹配的网 。
    • Click "Check" to submit your answer. Click "Next" to move onto another polyhedron.
      ::单击“ 检查” 以提交您的回答。 单击“ 下一步” 以移动到另一个多面体上 。
    • When you have matched all the polyhedra to their nets, you can continue using the arrows to explore the nets. Compare polyhedra with their nets by clicking "Fold" and "Unfold".
      ::当您将所有的聚环己烷与他们的网匹配后, 您可以继续使用箭头来探索网。 点击“ 折叠” 和“ 折叠 ” , 比较聚环己烷和他们的网 。
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    Properties of Polyhedra
    ::复面体的属性

    The three parts of a polyhedron are faces, edges , and vertices . A face is a polygonal side of a polyhedron. An edge is  a line segment where two faces meet. A vertex , or corner, is a point where two or more edges  meet.
    ::多面形的三部分是面、边缘和顶部。一面是多面形的多边形。一边缘是两面相交的线条段。顶部或角是两个或两个以上边缘相交的点。

    Use the interactive below to observe the relationship between faces, edges, and vertices.
    ::使用下面的交互效果观察面、边缘和顶点之间的关系。

     

    INTERACTIVE
    Nets
    minimize icon
    • Choose one of the polyhedra from the dropdown menu.
      ::从下拉菜单中选择一个 monhedra 。
    • Click the buttons to fold and unfold the net.
      ::单击按钮折叠并展开网。
    • Drag the screen to change your point of view. Use two fingers on your trackpad or touch screen or scroll the mouse wheel to zoom.
      ::拖曳屏幕以改变您的视图点。 在您的跟踪板上使用两根手指或触摸屏幕或滚动鼠标方向盘以缩放 。
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    In the interactive below, you will out a table to find the relationship between the number of parts of different polyhedral by counting the number of faces, vertices and edges for each.
    ::在下文互动部分中,您将拿出一张表格,通过计算每个多面体、脊椎和边缘的面部、脊椎和边缘的数量,查找不同多面体各部分数量之间的关系。

     

    INTERACTIVE
    Properties of Polyhedra Table
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    • Fill in the table with the correct number of faces, vertices, and edges for each shape by entering into the white boxes.
      ::输入白箱,填充表格中每个形状的正面、顶点和边缘的正确数量。
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    Discussion Question
    ::讨论问题

    Can you find a relationship between the faces, vertices, and edges?
    ::你能在脸部、脊椎和边缘之间找到一种关系吗?

     

     Summary
    ::摘要

    • A polyhedron is a closed solid made up of polygonal faces .
      ::一面体是由多边形面组成的封闭固体。
    • A net is  the 2-dimensional pattern that results from unfolding a solid . Nets show all the polygons that make up the faces of a solid.
      ::网是一个二维的图案,它来自一个固体。网显示了构成固体面孔的所有多边形。
    • The relationship between the number of faces, vertices, and edges on a polyhedron is  F + V − E = 2.  
      ::面部、顶点和多面形边缘之间的关联是 F+V-E=2 。