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Dedhert.Jr (talk | contribs) →Properties: says what is "it"? |
Dedhert.Jr (talk | contribs) Undid revision 1304815435 by LucasBrown (talk) The fact per se, WP:SHORTDESC delineate the eschew of gobbledygooks. Wherefore reestablish in lieu? Ditto for Cube. |
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| symmetry = <math>D_{3\mathrm{h}}</math>
| vertex_config = <math>3\times 3^4+6\times 3^5</math>
| dual = [[Associahedron
| angle = 109.5°<br>144.7°<br>169.5°
| properties = [[convex polytope|convex]],<br>[[composite polyhedron|composite]]
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can be derived by slicing it into a central prism and three square pyramids, and adding their volumes.{{r|berman}}
[[File:Triaugmented triangular prism (geodesic nets).svg|thumb|upright=1.2|Two unfolded nets of the triaugmented triangular prism, showing its two types of closed
The triaugmented triangular prism has two types of [[closed geodesic]]s. These are paths on its surface that are locally straight: they avoid vertices of the polyhedron, follow line segments across the faces that they cross, and form [[complementary angles]] on the two incident faces of each edge that they cross. One of the two types of closed geodesic runs parallel to the square base of a pyramid, through the eight faces surrounding the pyramid. For a polyhedron with unit-length sides, this geodesic has length <math>4</math>. The other type of closed geodesic crosses ten faces, and has length <math>\sqrt{19}\approx 4.36</math>. For each type there is a continuous family of parallel geodesics, all of the same length.{{r|lptw}}
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