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This work extends the theory of reciprocal diagrams in graphic statics toframeworks that are invariant under finite group actions by utilizing thehomology and representation theory of cellular cosheaves, recent tools fromapplied algebraic topology. By introducing the structure of an equivariantcellular cosheaf, we prove that pairs of self-stresses and reciprocal diagramsof symmetric frameworks are classified by the irreducible representations ofthe underlying group. We further derive the symmetry-aligned Eulercharacteristics of a finite dimensional equivariant chain complex, which forthe force cosheaf yields a new formulation of the symmetry-adapted Maxwellcounting rule for detecting symmetric self-stresses and kinematic degrees offreedom in frameworks. A freely available program is used to implement therelevant cosheaf homologies and illustrate the theory with examples.

Equivariant Cosheaves and Finite Group Representations in Graphic Statics