Phil's Polygonal Diameter Theorem:
GXWeb decagon playground

Online Encyclopedia of Integer Sequences: A357442

Consider a clock face with 2*n "hours" marked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections.

OR...

Given a 2n-gon...

You are to draw n diagonals so that they don't share end points, and there are an odd number of polygon sides between the end-points.

For n = 5 (decagon):

[1,1,1,9,9],

[9,3,1,1,1],

[1,1,5,9,9],

[1,3,5,3,7]

[3,5,7,3,3],

[7,3,7,3,3],

[7,5,1,9,9],

[7,5,3,5,5]

[9,7,5,3,1],

[5,5,1,5,1],

[5,5,5,5,5],

App generated by Geometry Expressions

Phil's Polygonal Diameter Theorem: GXWeb decagon playground

Phil's Polygonal Diameter Theorem:
GXWeb decagon playground