Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 2, 259-281.
Spaces of Stresses, Projections and Parallel
Drawings for Spherical Polyhedra
Henry Crapo, Walter Whiteley
Abstract.
Our first paper [1] 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: \item{(i)} \ isomorphisms between
\itemitem{ (a)} the affine space of polyhedra with a fixed projection;
\itemitem{ (b)} the vector space of self stresses of the framework; and
\itemitem{ (c)} the space of reciprocal figures of the framework (with one
fixed vertex);
\item{(ii)} \ and dually, appropriate maps between
\itemitem{ (d)} the vector space of parallel drawings of spatial polyhedral
surfaces,
\itemitem{ (e)} the space of frameworks with a fixed reciprocal, and
\itemitem{ (f)} the space of parallel drawings (infinitesimal motions) of
the projections.