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Spaces of stresses, projections and parallel drawings for spherical polyhedra. (English) Zbl 0819.52018

Summary: Our first paper [Topology Struct. 20, 55-79 (1993; Zbl 0793.52006)] analyzed the basic three way connection among static self stresses of plane frameworks, reciprocal diagrams and spatial oriented polyhedra. We extend this pattern to describe new:
(i) isomorphisms between
(a) the affine space of polyhedra with a fixed projection;
(b) the vector space of self stresses of the framework; and
(c) the space of reciprocal figures of the framework (with one fixed vertex);
(ii) and dually, appropriate maps between
(d) the vector space of parallel drawings of spatial polyhedral surfaces,
(e) the space of frameworks with a fixed reciprocal, and
(f) the space of parallel drawings (infinitesimal motions) of the projections.

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)

Citations:

Zbl 0793.52006
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