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I couldn't find this by way of the search log- if someone's dakka search-fu is better, feel free to direct me.
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A unit of Bikes that infiltrate in with Shrike, starting 18........001" away from an enemy unit.

The lead bike has the long edge of his base facing towards the enemy.

At the start of the turn, the bike pivots to face the enemy, putting him 1/8-1/4" closer (and, of course, allowing a 12" move and 6" charge to reach the enemy).
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Are non-circular bases allowed to pull the "pivot trick" the way some vehicles do?

(Yes, it's shady/against the spirit of the rules... I feel the same about vehicles doing it, but looking for a RAW basis to make a decision on, please)

The rules allow it, so yes.