FHP-III [8] is an extension of FHP-II which allows all collisions which conserve mass and momentum at each site. There are 76 possible collisions: 15 two-particle collisions of type (a), (c) and (d); 23 three-particle collisions of type (b), (e) and (f); 23 four-particle collisions and 15 five-particle collisions. The four- and five-particle collisions are the dual of the three- and two-particle collisions respectively. The dual of a collision is found by adding particles to the empty links and removing particles from the links which were originally filled. Example (g) is the dual of example (f). There are a total of 18 collisions of type (f) which can be considered to be collisions of type (a) or (c) with a spectator particle (a particle which does not take part in the collision and which continues travelling in a straight line). The two possible outcomes of collision (f) arise from these two different ways of viewing the collision. The one restriction which is commonly applied to the FHP-III model is that collisions (b) and (e) are not interchangeable, that is the (e) in-state can not collide to give the (b) out-state even though this conserves mass and momentum. This restriction do not affect the properties of the model but simplifies its implementation since it restricts the maximum possible number of out-states, for each in-state, to two. The FHP-III collision at non boundary sites are reproduced in full in appendix B.