This is an exercise in pure statics of the sort that Aristotle knew.
Imagine a rigid frame structure consisting of a unit octahedron whose coordinates are
<±1, 0, 0>, <0, ±1, 0>, <0, 0, ±1>.
Only the edges of the octahedron are present.
The entire octahedron is rigid if the 12 edges remain at a constant length of sqrt(2).
The three vertices with a positive coordinate we call the “+ set” and we call the others the “− set”. Forces applied to the + set vertices will not move them if the − set vertices are held fixed. Six well defined forces will appear at the six edges spanning the + set and the − set. Each of these forces will be in the direction of the respective edge. Six stress gauges on these respective edges thus measure and define the forces between the + set and the − set. I work out the equations here relating those 6 numbers with more conventional ways of defining forces between two portions of one rigid body. I imagine a rigid handle, perhaps spherical, attached to the +1 vertices while the three −1 vertices attached to something immovable, or later on, to a robot arm.
Assume that the spherical handle has <0,0,0> as its center. A unit compressive force between <−1, 0, 0> and <0, 1, 0> is equivalent to a force of <−1, 1, 0>/sqrt(2) thru the center along with a unit torque along the <0, 0, 1> axis. A force <1, 0, 0> will result in the following forces of the six connectors: