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168 lines
5.9 KiB
HTML
168 lines
5.9 KiB
HTML
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<title>Vertices, Edges and Faces</title>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Vertices, Edges and Faces</h1>
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<p class="center"><img src="images/vertex-edge-face.svg" alt="Vertex, Edge and Face" /><br>
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<span class="larger">A vertex is a corner.<br>
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An edge is a line segment between faces.<br>
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A face is a single flat surface<b></b></span>.</p>
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<p>Let us look more closely at each of those:</p>
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<h2>Vertices</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/vertex.svg" alt="Vertex" /></p>
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<p>A <b>vertex</b> (plural: <b>vertices</b>) is a point where two or more line segments meet.</p>
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<p class="center">It is a Corner.</p>
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<p>This <a href="tetrahedron.html">tetrahedron</a> has 4 vertices.</p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td align="right">And this <a href="pentagon.html">pentagon</a> has 5 vertices:</td>
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<td align="right"> </td>
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<td align="right"><img src="images/pentagon-vertices.svg" alt="Pentagon vertices" /></td>
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<td> </td>
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</tr>
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</table>
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<h2>Edges</h2>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/pentagon-edges.svg" alt="Pentagon edges" /><br>
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<span class="larger">This Pentagon<br>
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Has 5 Edges</span></p>
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<p> </p>
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<p>For a <b>polygon</b> an edge is a line segment <b>on the boundary</b> joining one vertex (corner point) to another.</p>
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<div style="clear:both"></div><br>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/edges.svg" alt="Edges" /><br>
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<span class="larger">This Tetrahedron<br>
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Has 6 Edges</span></p>
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<p> </p>
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<p>For a <b>polyhedron</b> an edge is a line segment where <b>two faces meet</b>.</p>
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<div style="clear:both"></div>
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<h2>Faces</h2>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/faces.svg" alt="Faces" /></td>
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<td>
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<p>A face is any of the individual flat surfaces of a solid object.</p>
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<p>This tetrahedron has 4 faces (there is one face you can't see)</p>
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<p> </p>
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</td>
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</tr>
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</table>
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<h2>Sides</h2>
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<p>"Side" is not a very accurate word, because it can mean:</p>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/side.svg" alt="Sides"></p>
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<ul>
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<li>An <b>edge</b> of a polygon, <b>or</b></li>
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<li>A <b>face</b> of a polyhedron</li>
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</ul>
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<h2>Euler's Formula</h2>
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<div class="center80">
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<p><b>For many solid shapes the</b></p>
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<ul>
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<li><b>Number of Faces</b></li>
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<li>plus the <b>Number of Vertices</b></li>
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<li>minus the <b>Number of Edges</b></li>
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</ul>
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<p><b>always equals 2</b></p>
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</div>
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<p class="center larger">This can be written: <b>F + V − E = 2</b></p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="images/poly-cube.svg" alt="cube" height="150" /></td>
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<td>
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<p>Try it on the cube:</p>
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<p>A cube has 6 Faces, 8 Vertices, and 12 Edges,</p>
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<p class="center">so:</p>
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<p class="center larger">6 + 8 − 12 = <b>2</b></p>
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<p>(To find out more about this read <a href="eulers-formula.html">Euler's Formula</a>.)</p>
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</td>
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</tr>
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</table>
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<p> </p>
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<div class="questions">
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<script>
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getQ(4994, 4995, 385, 2564, 372, 386, 390, 391, 2479, 2563);
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</script> </div>
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<div class="related">
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<a href="../platonic_solids.html">Platonic Solids</a>
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<a href="index.html">Geometry Index</a>
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</div>
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</article>
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Copyright © 2020 MathsIsFun.com
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