Star of Kobol
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The Star of Kobol is an award bestowed at the Quorum of Twelve's discretion. According to Sire Domra in his speech to Commander Adama, such an award was an honor that no "living Colonist had been given in over a millennium".
The Quorum gives this award to Adama in order to sugarcoat the fact that they are relieving Adama over unilateral control of the Fleet (Baltar's Escape).
Note
The award may represent the star of Kobol's system, that guided travelers (both in legend and in "Lost Planet of the Gods") through the great magnetic void to Kobol. As such the award might indicate that the recipient is a guiding beacon of light, leading the way for others.