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On this page are all constructions for C4[ 24, 7 ]. See Glossary for some detail.
HC(F4) =
SDD(Octahedron) = BGCG(Octahedron, 1; K2) = BGCG(W(6, 2), 2; C1) = BGCG(R_6(5, 4), 2; C1) = BGCG(R_6(5, 4), 3; C1)