The [[closed geodesic]]s of a polyhedron meanare the pathpaths 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}}
