What is the difference between an external spline and torx?

What geometry the hole of a Allen wrench?

The hole, which is six sided, is actually in the head of the Allen screw or bolt, NOT in the wrench. The Allen wrench is a six sided tool steel bar made to very precise measurements and often, but not always, bent at a right angle at one end. Professional Allen wrenches almost always have a large 'T' handle to use as a grip, and are about 7-9 inches long, as opposed to the smaller ones you find in hardware stores. The Allen wrench principle is to allow more torque on the screw or bolt. Many mechanics even have an entire set of Allen bits to fit on their torque wrench. Variations on the well known Allen head, (which has been around since 1912) are the modern Torx screw and the Bristol screw (much used in British aircraft industry) - All of these have a similar shape and a common principle of allowing more torque to be applied, and avoiding what is called 'cam out'.