Tetrahedral Spaceships
 A conventional ship turns with attitude jets and thus has a turning radius. It would be desirable to eliminate the turning radius. This can be done if there are several thrusters. But thrusters are expensive and add more mass to the spaceship. The minimum number of thrusters that could accelerate the ship in any direction would be 4.

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 Although you can instantly accelerate in any direction, it can be wasteful. For example, when you reverse direction using three thrusters, 2/3 of the thrust is wasted since the jets oppose each other to some extent.

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 It is desirable to have attitude jets. Here is a design that places three attitude jets alongside a main thruster. With attitude jets, the maximum angle you'd have to turn a main thruster would be 70.5 degrees, which is an improvement over the conventional 180 degrees.

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 The attitude jets shown earlier don't provide a lot of torque. The further the jet is from the axis of symmetry it runs parrallel to, the more torque. Above is a design for maximizing attitude jet torque.

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 With attitude jets, a craft could move in any direction with only one thruster, as conventional craft do. If the tetship's thrusters were detachable, mass could be shed by jettisoning up to three thrusters.  When systems can fail, redundancy is desirable. Since the ship has 4 thrusters, it has much less  chance of being stranded in space from rocket failure. I got this idea from a sci.math thread where Kirby Urner pointed out you can describe 3 space with positive multiples of 4 vectors. I later learned that Kirby also has come up with the notion of tetrahedral spaceships and calls them Quadpods.

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