KeywordsGoldberg polyhedra; cages; fullerenes; tilings; cutouts; regular polyhedron; chiral polyhedron; net; eccentricity; center; periphery; average eccentricity; regular polyhedra; reflection group; fundamental region; invariant mapping; polyhedra; isoperimetric problem; point group symmetry; Coxeter diagrams; irregular chiral polyhedra; quaternions; snub cube; snub dodecahedron; complex crystals; quasicrystals; nested clusters; crystal growth; polyhedra; panoramic projection; shadow construction; Computer Aided Design (CAD); descriptive geometry; maps on surfaces; map; oriented map; truncation; dual; medial; snub; flag graph; arc graph