Why does Philae have only three legs? Can anyone explain why comet lander Philae has only three legs? Isn't it obvious that it now has problems that it would not have had if it had four legs arranged as a regular tetrahedron - or even more legs? Were legs so expensive?
 A: Have you ever sat on a wobbly, four-legged chair? That can't happen with a three-legged chair. A three-legged chair is stable. Four legs is one leg too many. A four-legged lander would need to adjust the lengths of the legs to stabilize it.
Update
Aside: The English word you are seeking is tetrahedron. Now that the intent of the question is clear, the answer is no. Adding a fourth leg to Philae so it could land in any orientation wouldn't work because Philae has a preferred orientation. There would be no point in adding the capability to land in some other orientation because many of the experiments on the wouldn't be able to function. Philae has a definite "up" and "down".
Second update
A tetrahedral object can land in four different orientations. Only one of those orientations is useful because Philae has a definite "up" and "down". There would be no point in adding a fourth tetrahedral leg without the ability to reorient the central body of the vehicle. That adds considerable complexity to the vehicle.
The reason Philae had problems was because its simple harpoon system and its simple thruster system failed. BTW, those harpoons and that thruster were part of what gave Philae a definite "up" and "down". As was seen with Philae, even simple stuff has an unfortunately high propensity to fail in spacecraft. Complex stuff? That fails with even greater propensity. Spacecraft designers have learned this lesson many times over and regularly have to tell themselves to "keep it simple, stupid!" The KISS principle is driving concept in designing space vehicles.
