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method="get" action="/search/" name="search" id="search-mobile" accept-charset="UTF-8"> <input type="text" name="query" placeholder="Search" id="searchFieldMobile"> <img src="/images/header/search-icon.png" width="18" height="18" id="mobile-search" class="search-btn" title="Search" alt="Search" onclick="submitForm()"> </form> <nav class="topics-nav"> <a href="/topics/Algebra.html" id="sidebar-algebra"> Algebra </a> <a href="/topics/AppliedMathematics.html" id="sidebar-appliedmathematics"> Applied Mathematics </a> <a href="/topics/CalculusandAnalysis.html" id="sidebar-calculusandanalysis"> Calculus and Analysis </a> <a href="/topics/DiscreteMathematics.html" id="sidebar-discretemathematics"> Discrete Mathematics </a> <a href="/topics/FoundationsofMathematics.html" id="sidebar-foundationsofmathematics"> Foundations of Mathematics </a> <a href="/topics/Geometry.html" id="sidebar-geometry"> Geometry </a> <a href="/topics/HistoryandTerminology.html" id="sidebar-historyandterminology"> History and Terminology </a> <a href="/topics/NumberTheory.html" id="sidebar-numbertheory"> Number Theory </a> <a href="/topics/ProbabilityandStatistics.html" id="sidebar-probabilityandstatistics"> Probability and Statistics </a> <a href="/topics/RecreationalMathematics.html" id="sidebar-recreationalmathematics"> Recreational Mathematics </a> <a href="/topics/Topology.html" id="sidebar-topology"> Topology </a> </nav> <nav class="secondary-nav"> <a href="/letters/"> Alphabetical Index </a> <a href="/whatsnew/"> New in MathWorld </a> </nav> </section> <section id="content">  <nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/Geometry.html">Geometry</a> </li> <li> <a href="/topics/SolidGeometry.html">Solid Geometry</a> </li> <li> <a href="/topics/MiscellaneousSolids.html">Miscellaneous Solids</a> </li> </ul></nav>   <h1>Haűy Construction</h1>  <hr class="margin-t-1-8 margin-b-3-4">  <div class="attachments text-align-r"> <a href="/notebooks/Polyhedra/HauyConstruction.nb" download="HauyConstruction.nb"><img src="/images/entries/download-notebook-icon.png" width="26" height="27" alt="DOWNLOAD Mathematica Notebook" /><span>Download <span class="display-i display-n__600">Wolfram </span>Notebook</span></a> </div>  <div class="entry-content"> <div class="center-image"> <img style="max-width:100%;max-height:100%;" width="568.48" src="images/eps-svg/HauyConstruction_1000.png" class="" alt="HauyConstruction" /> </div> <p> The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the <a href="/Cuboctahedron.html">cuboctahedron</a>, <a href="/Octahedron.html">octahedron</a> <a href="/RhombicDodecahedron.html">rhombic dodecahedron</a>, and <a href="/SquarePyramid.html">square pyramid</a>. In Book XIII of the <i><a href="/Elements.html">Elements</a></i>, Euclid used a Haűy construction to build the <a href="/Dodecahedron.html">dodecahedron</a> (Wells 1991). </p> </div>  <hr class="margin-b-1-1-4"> <div class="c-777 entry-secondary-content">  <h2>See also</h2><a href="/OctahedralNumber.html">Octahedral Number</a>, <a href="/Octahedron.html">Octahedron</a>, <a href="/RhombicDodecahedralNumber.html">Rhombic Dodecahedral Number</a>, <a href="/RhombicDodecahedron.html">Rhombic Dodecahedron</a>       <h2>Explore with Wolfram|Alpha</h2> <div id="WAwidget"> <div class="WAwidget-wrapper"> <img alt="WolframAlpha" title="WolframAlpha" src="/images/wolframalpha/WA-logo.png" width="136" height="20"> <form name="wolframalpha" action="https://www.wolframalpha.com/input/" target="_blank"> <input type="text" name="i" class="search" placeholder="Solve your math problems and get step-by-step solutions" value=""> <button type="submit" title="Evaluate on WolframAlpha"></button> </form> </div> <div class="WAwidget-wrapper try"> <p class="text-align-r"> More things to try: </p> <ul> <li> <a target="_blank" href="http://www.wolframalpha.com/entities/solids/cork_plug/92/mr/84/"> cork plug </a> </li> <li><a target="_blank" href="https://www.wolframalpha.com/input/?i=%28%283%2B4i%29%2F5%29%5E10">((3+4i)/5)^10</a></li> <li><a target="_blank" href="https://www.wolframalpha.com/input/?i=corners+%7Cx%5E3+-+2x%5E2+-+16x+%2B+6%7C">corners |x^3 - 2x^2 - 16x + 6|</a></li> </ul> </div> </div>   <h2>References</h2><cite>Haűy, R.-J. "Essai d'une théorie sur la structure des crystals appliquée à plusieurs genres de substances crystallisées." 1784.</cite><cite>Wells, D. <i><a href="http://www.amazon.com/exec/obidos/ASIN/0140118136/ref=nosim/ericstreasuretro">The Penguin Dictionary of Curious and Interesting Geometry.</a></i> London: Penguin, p. 93, 1991.</cite><h2>Referenced on Wolfram|Alpha</h2><a href="http://www.wolframalpha.com/entities/mathworld/ha%C5%B1y_construction/uw/gt/zi/" title="Haűy Construction" target="_blank">Haűy Construction</a>   <h2>Cite this as:</h2> <p> <a href="/about/author.html">Weisstein, Eric W.</a> "Haűy Construction." From <a href="/"><i>MathWorld</i></a>--A Wolfram Web Resource. <a href="https://mathworld.wolfram.com/HauyConstruction.html">https://mathworld.wolfram.com/HauyConstruction.html</a> </p>  <h2>Subject classifications</h2><nav class="breadcrumbs"><ul class="breadcrumb"> <li> <a href="/topics/Geometry.html">Geometry</a> </li> <li> <a href="/topics/SolidGeometry.html">Solid Geometry</a> </li> <li> <a href="/topics/MiscellaneousSolids.html">Miscellaneous Solids</a> </li> </ul></nav>  </div> </section> </section>  </div> </main> <aside id="bottom"> <style> #bottom { padding-bottom: 65px; } #acknowledgment { display:none; } .attribution { font-size: .75rem; font-style: italic; } footer ul li:not(:last-of-type)::after { background: #a3a3a3; margin-left: .3rem; margin-right: .1rem; } @media all and (max-width: 900px) { .attribution { font-size: 12px; } } @media (max-width: 600px) { footer { max-width: 360px; } footer ul { max-width: 360px; } footer ul:nth-child(1) li:nth-child(2):after { content: ""; height: 11px; } footer ul:nth-child(1) li:nth-child(3):after { content: ""; height: 0px; } } </style> <footer> <ul> <li><a href="/about/">About MathWorld</a></li> <li><a href="/classroom/">MathWorld Classroom</a></li> <li><a href="/contact/">Contribute</a></li> <li><a href="https://www.amazon.com/exec/obidos/ASIN/1420072218/ref=nosim/weisstein-20" target="_blank">MathWorld Book</a></li> <li class="display-n display-ib__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> </ul> <ul> <li class="display-n__600"><a href="/whatsnew/">13,247 Entries</a></li> <li class="display-n__600"><a href="/whatsnew/">Last Updated: Mon Feb 24 2025</a></li>  <li><a href="https://www.wolfram.com" target="_blank">©1999–2025 Wolfram Research, Inc.</a></li> <li><a href="https://www.wolfram.com/legal/terms/mathworld.html" target="_blank">Terms of Use</a></li> </ul> <ul class="wolfram"> <li class="display-n__600 display-n__900"><a href="https://www.wolfram.com" target="_blank" aria-label="Wolfram"><img src="/images/footer/wolfram-logo.png" alt="Wolfram" title="Wolfram" width="121" height="28"></a></li> <li class="display-n__600"><a href="https://www.wolfram.com" target="_blank">wolfram.com</a></li> <li class="display-n__600"><a href="https://www.wolfram.com/education/" target="_blank">Wolfram for Education</a></li> <li class="attribution">Created, developed and nurtured by Eric Weisstein at Wolfram Research</li> </ul> </footer> <section id="acknowledgment"> <i>Created, developed and nurtured by Eric Weisstein at Wolfram Research</i> </section> </aside> <script type="text/javascript" src="/scripts/scripts.js"></script> <script src="/common/js/c2c/1.0/WolframC2C.js"></script> <script src="/common/js/c2c/1.0/WolframC2CGui.js"></script> <script src="/common/js/c2c/1.0/WolframC2CDefault.js"></script> <link rel="stylesheet" href="/common/js/c2c/1.0/WolframC2CGui.css.en"> <style> .wolfram-c2c-wrapper { padding: 0px !important; border: 0px; } .wolfram-c2c-wrapper:active { border: 0px; } .wolfram-c2c-wrapper:hover { border: 0px; } </style> <script> let c2cWrittings = new WolframC2CDefault({'triggerClass':'mathworld-c2c_above', 'uniqueIdPrefix': 'mathworld-c2c_above-'}); </script> <style> #IPstripe-outer { background: #47a2af; } #IPstripe-outer:hover { background: #0095aa; } </style> <div id="IPstripe-wrap"></div> <script src="/common/stripe/stripe.en.js"></script> </body> </html>