Middleton-on-Lune railway station Middleton-on-Lune railway station Middleton-on-Lune railway station was located in Westmorland (now Cumbria), serving the hamlet and rural locale of Middleton on the Ingleton Branch Line. It was opened as Middleton in 1861 and renamed Middleton-on-Lune on 19 July 1926, closing in 1931. The Lancaster and Carlisle Railway built the Ingleton Branch Line from the existing Ingleton Station to . By the time the branch was completed in 1861, the L&CR was operated by the London and North Western Railway (L&NWR). After formal closure the line was still on occasions used for weekend excursions and to transport pupils to and from
Spherical lune the second half great circle has moved a full circle, and the lune in between covers the sphere as a spherical monogon — the area formula for the spherical lune gives 4π"R", the surface area of the sphere. A hosohedron is a tessellation of the sphere by lunes. A n-gonal regular hosohedron, {2,n} has "n" equal lunes of π/"n" radians. An "n"-hosohedron has dihedral symmetry D, ["n",2], (*22"n") of order 4"n". Each lune individually has cyclic symmetry "C", [2], (*22) of order 4. Each hosohedra can be divided by an equatorial bisector into two equal spherical triangles. The visibly lighted