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Dedhert.Jr (talk | contribs) closed geodesics; not sure how understandable is this? a little enlightment? |
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\frac{\pi}{3}+\arccos\left(-\frac13\right)&\approx 169.5^\circ.\\
\end{align}</math>
The [[closed geodesic]]s of a polyhedron mean the path on the surface avoiding the vertices and locally look like the shortest path. In other words, the path follows straight line segments across each face that intersect, and creates complementary angles on the two incident faces of the edge as it crosses. In the case of a triaugmented triangular prism, and with unit-length, it has two types of closed geodesics, the first geodesic crosses the edges of two equilateral square pyramids and a triangular prism, an [[equator]] of the solid, with length of <math> 4 </math>; the second geodesic crosses the edges of three equilateral square pyramids, with length of <math> \sqrt{19} </math>.{{r|lptw}}
== Fritsch graph ==
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| title = A simple sphere theorem for graphs
| year = 2019}}</ref>
<ref name=lptw>{{citation
| last1 = Lawson | first1 = Kyle A.
| last2 = Parish | first2 = James L.
| last3 = Traub | first3 = Cynthia M.
| last4 = Weyhaupt | first4 = Adam G.
| doi = 10.12732/ijpam.v89i2.1
| issue = 2
| journal = International Journal of Pure and Applied Mathematics
| pages = 123–139
| title = Coloring graphs to classify simple closed geodesics on convex deltahedra.
| volume = 89
| year = 2013
| zbl = 1286.05048 | url = https://ijpam.eu/contents/2013-89-2/1/1.pdf
| doi-access = free
}}.</ref>
<ref name=pugh>{{citation
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