Monogon

<h2 id="in-euclidean-geometry">In Euclidean geometry</h2>
<p>In <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a> a <i>monogon</i> is a <a href="/facts/Degeneracy_(mathematics)/BqhqlXPH">degenerate</a> polygon because its endpoints must coincide, unlike any Euclidean line segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon.
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<h2 id="in-spherical-geometry">In spherical geometry</h2>
<p>In <a href="/facts/Spherical_geometry/WGLQb1Ys">spherical geometry</a>, a monogon can be constructed as a vertex on a <a href="/facts/Great_circle/x4fq6eNm">great circle</a> (<a href="/facts/Equator/CjaxbVaN">equator</a>). This forms a <a href="/facts/Dihedron/YkNgovlv">dihedron</a>, {1,2}, with two hemispherical monogonal faces which share one 360° edge and one vertex. Its dual, a <a href="/facts/Hosohedron/t2dyV0bW">hosohedron</a>, {2,1} has two <a href="/facts/Antipodal_point/2V3228jA">antipodal</a> vertices at the poles, one 360° <a href="/facts/Lune_(mathematics)/2h1Tb5l7">lune</a> face, and one edge (meridian) between the two vertices.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
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<table><tbody><tr><td>Monogonal <a href="/facts/Dihedron/YkNgovlv">dihedron</a>, {1,2}</td><td>Monogonal <a href="/facts/Hosohedron/t2dyV0bW">hosohedron</a>, {2,1}</td></tr></tbody></table>
<h2 id="see-also">See also</h2>

Look up <i>monogon</i> in Wiktionary, the free dictionary.

<ul><li><a href="/facts/Digon/vur5IQ5d">Digon</a></li></ul>

<ul><li><a href="/facts/Herbert_Busemann/PR46wsFS">Herbert Busemann</a>, The geometry of geodesics. New York, Academic Press, 1955</li>
<li>Coxeter, H.S.M; <i>Regular Polytopes</i> (third edition). Dover Publications Inc. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-61480-8</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Coxeter, Introduction to geometry, 1969, Second edition, sec 21.3 Regular maps, p. 386-388 <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
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Monogon open-in-new

Monogon