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<!doctype html> <html lang="en"> <head> <meta charset="UTF-8">  <title>Spinning Octahedron</title> <meta name="description" content="A 3D shape with 8 flat faces. Notice these interesting things: It has 8 Faces. It has 12 Edges. It has 6 Vertices (corner points).">  <link rel="canonical" href="https://www.mathsisfun.com/geometry/octahedron.html"> <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebPage", "url": "https://www.mathsisfun.com/geometry/octahedron.html", "name": "Spinning Octahedron", "description": "A 3D shape with 8 flat faces. Notice these interesting things: It has 8 Faces. It has 12 Edges. It has 6 Vertices (corner points).", "image": "https://www.mathsisfun.com/geometry/images/poly-octahedron-hdr.png", "publisher": { "@type": "Organization", "name": "Math Is Fun", "url": "https://www.mathsisfun.com" }, "mainEntity": { "@type": "Article", "headline": "Spinning Octahedron", "description": "A 3D shape with 8 flat faces. Notice these interesting things: It has 8 Faces. It has 12 Edges. It has 6 Vertices (corner points).", "author": { "@type": "Person", "name": "Rod Pierce" }, "image": "https://www.mathsisfun.com/geometry/images/poly-octahedron-hdr.png" } } </script> <meta property="og:title" content="Spinning Octahedron"> <meta property="og:description" content="A 3D shape with 8 flat faces. Notice these interesting things: It has 8 Faces. It has 12 Edges. It has 6 Vertices (corner points)."> <meta property="og:type" content="article"> <meta property="og:site_name" content="Math is Fun"> <meta property="og:url" content="https://www.mathsisfun.com/geometry/octahedron.html"> <meta property="og:image" content="https://www.mathsisfun.com/geometry/images/poly-octahedron-hdr.png"> <meta name="keywords" content="math, maths, mathematics, school, homework, education"> <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes"> <meta name="HandheldFriendly" content="true"> <meta name="referrer" content="always"> <link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin> <link rel="preload" href="../style4.css" as="style"> <link rel="preload" href="../main4.js" as="script"> <link rel="stylesheet" href="../style4.css"> <script src="../main4.js" defer></script> </head> <body id="bodybg"> <div id="stt"></div> <div id="adTop"></div> <header> <div id="hdr"></div> <div id="tran"></div> <div id="adHide"></div> <div id="cookOK"></div> </header> <div class="mid"> <nav> <div id="menuWide" class="menu"></div> <div id="logo"><a href="https://www.mathsisfun.com/"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div> <div id="themeChg"></div> <div id="search" role="search"></div> <div id="linkto"></div> <div id="menuSlim" class="menu"></div> <div id="menuTiny" class="menu"></div> </nav> <div id="extra"></div> <article id="content" role="main">  <h1 class="center">Octahedron</h1> <p class="center large">A <a href="solid-geometry.html">3D</a> shape with 8 flat faces.</p> <div class="script" style="height: 450px;"> images/polyhedra.js?mode=octahedron</div> <div class="fun"> <div class="head">Octahedron Facts</div> <div class="floatRt"><img src="images/poly-octahedron.svg" alt="octahedron" style="transform: scale(2);" height="86" width="85"></div> <p><b>Notice these interesting things:</b></p> <ul> <li>It has 8 faces</li> <li>It has 12 edges</li> <li>It has 6 vertices (corner points)</li> </ul> <p>When it is <a href="regular-polyhedra.html">regular</a>:</p> <ul> <li>Each face is an <a href="../triangle.html">Equilateral Triangle</a></li> <li>At each vertex 4 edges meet</li> <li>It is one of the <a href="../platonic_solids.html">Platonic Solids</a></li> </ul> </div> <h2>Volume and Surface Area</h2> <p>For a <a href="regular-polyhedra.html">regular</a> octahedron (where all faces are equilateral triangles):</p> <div class="two"> <div class="lt"><b>Surface Area</b> =</div> <div class="rt">2 × √3 × (Edge Length)<sup>2</sup></div> <div class="lt" style="margin-top: 5px;"><b>Volume</b> =</div> <div class="rt"><span class="intbl"><em>√2</em><strong>3</strong></span> × (Edge Length)<sup>3</sup></div> </div> <div class="words"> <p style="float:right; margin: 0 0 5px 10px;"><img src="images/poly-octahedron.svg" alt="Octahedron" height="86" width="85"></p> <p>The name <i>octahedron</i> comes from the Greek <i>octa-</i> meaning 8, because it is a <a href="polyhedron.html">polyhedron</a> with 8 faces. Like an <i>octopus</i> has 8 tentacles.</p> <p>When we have more than one octahedron they are called <b>octahedra</b></p> </div> <p> </p> <p style="float:left; margin: 0 10px 5px 0;"><img src="images/hexagonal-prism.jpg" alt="hexagonal prism" height="132" width="120"></p> <p>"Octahedron" usually means "<a href="regular-polyhedra.html">regular</a> octahedron" where all faces are identical equilateral triangles, but an octahedron can also be <b>irregular</b>.</p> <p>This shape is <b>also</b> an octahedron, even though all faces are not the same. But it is better called a hexagonal <a href="prisms.html">prism</a>.</p> <div style="clear:both"></div> <p> </p> <p style="float:right; margin: 0 0 5px 10px;"><img src="images/dice-octahedron.jpg" alt="dice octahedron" height="150" width="123"></p> <p><b>8-Sided Dice?</b> Yes! An octahedron that has 8 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> </p> <table style="border: 0; margin:auto;"> <tr> <td><a href="octahedron-model.html">Make your own Octahedron</a>,<br> cut out the shape and glue it together.</td> <td> <a href="octahedron-model.html"><img src="images/octahedron-model-thumb.svg" alt="Octahedron Model Template" height="219" width="294"></a></td> </tr> </table> <p><span class="large">Here is a beautiful fluorite crystal.</span> It naturally forms an octahedron, but this one is a "truncated" (tips chopped off) octahedron:</p> <div class="center"><img src="images/octahedral-fluorite.jpg" alt="octahedral fluorite" height="292" width="300"><br> <span class="small">Courtesy Wikimedia user CarlesMillan</span></div> <p> </p> <div class="questions">1856, 1857, 1858, 1859</div> <div class="related"> <a href="../platonic_solids.html">Platonic Solids</a> <a href="solid-geometry.html">Solid Geometry</a> </div>  </article> <div id="adend" class="centerfull noprint"></div> <footer id="footer" class="centerfull noprint"></footer> <div id="copyrt">Copyright © 2025 Rod Pierce</div> </div> </body>  </html>