Triaugmented triangular prism: Difference between revisions

Revision as of 19:20, 16 March 2025

Revision as of 19:22, 16 March 2025

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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 of the polyhedron faces, perpendicularly to an edge of each face; itand has length <math>\sqrt{19}\approx 4.36</math>.{{r|lptw}}

== Fritsch graph ==