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Hemicube Vectors?

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Hi. I am trying to render a hemicube for radiosity purposes. I have the point from which to render and the normalized vector pointing from the centre of the cube to the centre of the front side of the hemicube. Could someone please tell me how to calculate the vectors pointing to the other sides of the cube? The vector I have is not necessarily on one of the axii or on their planes. Thanks.

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