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Reference.org
Figurate number
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<p>The term figurate number is used by different writers for members of different sets of numbers, generalizing from <a href="/facts/Triangular_numbers/KHonHtQJ">triangular numbers</a> to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean </p> <ul><li><a href="/facts/Polygonal_number/7hBvthEr">polygonal number</a></li> <li>a number represented as a discrete r-dimensional regular <a href="/facts/Geometry/wTQf5ffQ">geometric</a> pattern of r-dimensional <a href="/facts/Ball_(mathematics)/f9vpMVMp">balls</a> such as a polygonal number (for <i>r</i> = 2) or a polyhedral number (for <i>r</i> = 3).</li> <li>a member of the subset of the sets above containing only triangular numbers, <a href="/facts/Pyramidal_numbers/tcRjsACG">pyramidal numbers</a>, and their analogs in other dimensions.</li></ul>