Finding tensegrity structures: Geometric and symbolic approaches. EACA 04.

Problem 1 . We are given five concrete points in general position in R^3;

p1 := (0; 0; 0); p2 := (1; 1; 1); p3 := (0; 1; 0); p4 := (1; 0; 0); p5 := (0; 0; 1) and a sixth one p6 := (x; y; z)
with unknown coordinates, to be determined under the conditions that the framework with vertices {p1; : : : ; p6} and edges

{p1; : : : ; p6}/2
minus

{p1p6; p2p4; p3p5}

stays in general position and admits a non-null self-stress.

Note that this is the same topological configuration of the oblique triangular prism.
Let us point up here that, for different particular coordinates of the first five points the problem can be solved from the ones chosen here using projective invariance (see [5, 11]).

Solucin geometrica

Solucin algebraica