-- Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
--
-- Triangle P3,n=n(n+1)/2 1, 3, 6, 10, 15, ...
-- Square P4,n=n2 1, 4, 9, 16, 25, ...
-- Pentagonal P5,n=n(3n1)/2 1, 5, 12, 22, 35, ...
-- Hexagonal P6,n=n(2n1) 1, 6, 15, 28, 45, ...
-- Heptagonal P7,n=n(5n3)/2 1, 7, 18, 34, 55, ...
-- Octagonal P8,n=n(3n2) 1, 8, 21, 40, 65, ...
-- The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
--
-- The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
-- Each polygonal type: triangle (P3,127=8128), square (P4,91=8281), and pentagonal (P5,44=2882), is represented by a different number in the set.
-- This is the only set of 4-digit numbers with this property.
-- Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.