The box dimensions of exceptional self-affine sets in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>

We study the box dimensions of self-affine sets in R3 which are generated by a finite collection generalised permutation matrices. obtain bounds for hold with very minimal assumptions and give rise to sharp results many cases. There issues extending well-established planar theory including that principal projections (affine distortions of) overlaps (rather than self-similar sets) natural modified singular value function fails be sub-multiplicative general. introduce several new techniques deal these hopefully provide some insight into challenges further.