Triaugmented triangular prism: Difference between revisions

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Properties: not perpendicular
Properties: parallel
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\end{align}</math>
 
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}}
 
== Fritsch graph ==