171

171 is the 18th triangular number and a Jacobsthal number. There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices. The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon. There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.