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<title>Spinning Icosahedron</title>
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<h1 class="center">Icosahedron</h1>
<div class="boxa">
<div class="head">Icosahedron Facts</div>
<p><b>Notice these interesting things:</b></p>
<ul>
<li>It has 20 Faces</li>
<li>Each face is an <a href="../triangle.html">Equilateral Triangle</a></li>
<li>It has 30 Edges</li>
<li>It has 12 Vertices (corner points)</li>
<li>and at each vertex 5 edges meet</li>
<li>It is one of the <a href="../platonic_solids.html">Platonic Solids</a></li>
</ul>
</div>
<div class="boxb">
<div class="script" style="height: 450px;">
images/polyhedra.js?mode=icosahedron
</div>
</div>
<h2>Volume and Surface Area</h2>
<p class="center"><b>Volume</b> = 5×(3+√5)/12 × (Edge Length)<sup>3</sup></p>
<p class="center"><b>Surface Area</b> = 5×√3 × (Edge Length)<sup>2</sup></p>
<div class="words">
<p>It is called an <i>icosahedron</i> because it is a polyhedron that has 20 faces (from Greek <i>icosa-</i> meaning 20)</p>
<p>When we have more than one icosahedron they are called <b>icosahedra</b></p>
</div>
<p>&nbsp;</p>
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/rhombic-icosahedron.gif" alt="rhombic icosahedron" height="80" width="100"></p>
<p>When we say "icosahedron" we often mean "regular icosahedron" (in other words all faces are the same size and shape), but it doesn't <i>have</i> to be - this is also an icosahedron, even though all faces are not the same.</p>
<div style="clear:both"></div>
<p>&nbsp;</p>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/dice-icosahedron.jpg" alt="dice icosahedron" height="150" width="138"></p>
<p><b>20-Sided Dice?</b> Yes! An icosahedron that has 20 equal faces has an equal chance of landing on any face.</p>
<p>In fact, you can make <a href="fair-dice.html">fair dice</a> out of all of the Platonic Solids.</p>
<div style="clear:both"></div>
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/hpv-icosahedron.gif" alt="hpv icosahedron" height="148" width="150"></p>
<p>&nbsp;</p>
<p>The outer shell of this virus (the Human papilloma virus) is like an icosahedron<br>
<span class="tiny">Courtesy of
VirusWorld at virology.wisc.edu</span></p>
<div style="clear:both"></div>
<table align="right" border="0">
<tbody>
<tr>
<td style="text-align:right;">The head of a bacteriophage (a virus that targets bacteria) is an icosahedron</td>
<td><span style="float:right; margin: 0 0 5px 10px;"><img src="images/bacteriophage.svg" alt="bacteriophage icosahedron head illustration" height="200" width="184"></span></td>
<td>&nbsp;</td>
<td><span style="float:right; margin: 0 0 5px 10px;"><img src="images/bacteriophage.jpg" alt="bacteriophage icosahedron head photo" height="199" width="122"></span></td>
</tr>
<tr>
<td>&nbsp;</td>
<td><span class="tiny">Illustration of bacteriophage</span></td>
<td>&nbsp;</td>
<td><span class="tiny">Photo courtesy of Wikpedia user Kuksi</span></td>
</tr>
</tbody></table><div style="clear:both"></div>
<p>&nbsp;</p>
<table style="border: 0; margin:auto;">
<tbody>
<tr>
<td><a href="icosahedron-model.html">Make your own Icosahedron</a>,<br>
cut out the shape and glue it together.</td>
<td>
<a href="icosahedron-model.html"><img src="images/icosahedron-model-thumb.svg" alt="Icosahedron Model Template" height="" width=""></a>
</td>
</tr>
</tbody></table>
<p>&nbsp;</p>
<div class="fun">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/icosahedron-truncated.gif" alt="rhombic icosahedron" height="160" width="163"></p>
<h3>Soccer Ball</h3>
<p>A soccer ball is <b>related</b> to an icosahedron:</p>
<p>It is a <a href="polyhedron-modelsa5cf.html?m=Truncated%20Icosahedron">truncated icosahedron</a> (truncated means it has bits chopped off it)</p>
<p>It has 12 pentagons and 20 hexagons</p>
</div>
<p>&nbsp;</p>
<p>&nbsp;</p>
<div class="questions">1852, 1853, 1854, 1855</div>
<div class="related">
<a href="../platonic_solids.html">Platonic Solids</a>
<a href="solid-geometry.html">Solid Geometry</a>
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