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Challenge 436: Anton's Dodecagon

Anton the ant makes a journey around a dodecagon...

Anton is at vertex A of a regular dodecagon ABCDEFGHIJKL. He wishes to visit a number of vertices, always walking in a straight line. The following routes are available:

(1) The "Grand Tour" - Anton visits all 12 vertices in order.

(2) The "Big Tour" - Anton visits every 3rd vertex, i.e. D, G, J then back to A.

(3) The "Mini Tour" - Anton visits every 4th vertex, i.e. E, I then back to A.

(4) The "Micro Tour" - Anton visits every 6th vertex, i.e. G then back to A.

Anton considers either a Grand Tour followed by a Micro Tour, or a Big Tour followed by a Mini Tour.

Without using a calculator, find which option is longer.