Question 1181720
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The octahedron has 8 faces, 6 vertices, and 12 edges; there are 4 edges meeting at each of the 6 vertices.<br>
Since the ant starts and ends at the top vertex and can't pass through that vertex during her walk, her trip can only travel on 2 of the 4 edges that meet at the top vertex.  So the maximum POSSIBLE number of edges she can travel on her walk is 10.<br>
And by trial and error, paths can be found on which she in fact travels the other 10 edges.<br>
So the maximum distance she can cover in her walk is 10 units.<br>