The figure shows a cube of side 1 on which all twelve face diagonals have been drawn – creating a network with 14 vertices (the original eight corners, plus the six face centres) and 36 edges (the original twelve edges of the cube plus four extra edges on each face). What is the exact length of the shortest path along the edges of the network which passes through all 14 vertices?
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6
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Intermediate Mathematical Challenge 2005 (2005)
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