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    Quasiregular Polyhedron

    Members

    cuboctahedron | icosidodecahedron

    Visual representations

    Combinatorial properties

    | vertices | edges | faces cuboctahedron | 12 | 24 | 14 (8 triangles, 6 quadrilaterals) icosidodecahedron | 30 | 60 | 32 (20 triangles, 12 pentagons)

    Edge lengths

    1 (24 edges)

    1 (60 edges)

    Geometric properties

    | volume cuboctahedron | (5 sqrt(2))/3 icosidodecahedron | 1/6 (45 + 17 sqrt(5)) | surface area cuboctahedron | 2 (3 + sqrt(3)) icosidodecahedron | sqrt(30 (10 + 3 sqrt(5) + sqrt(75 + 30 sqrt(5)))) | circumradius cuboctahedron | 1 icosidodecahedron | 1/2 (1 + sqrt(5)) | midradius cuboctahedron | sqrt(3)/2 icosidodecahedron | 1/2 sqrt(5 + 2 sqrt(5)) (assuming unit edge lengths)

    Schläfli symbol

    | cuboctahedron | icosidodecahedron Schläfli symbol | {3 4} | {3 5}

    Wythoff symbol

    | cuboctahedron | icosidodecahedron Wythoff symbol | 2|3 4 | 2|3 5

    Nets

    Skeleton graphs

    | skeleton graph name cuboctahedron | cuboctahedral graph icosidodecahedron | icosidodecahedral graph

    Dual polyhedra

    | dual name cuboctahedron | rhombic dodecahedron icosidodecahedron | rhombic triacontahedron

    Dual skeleton graphs

    | dual skeleton name cuboctahedron | rhombic dodecahedral graph icosidodecahedron | rhombic triacontahedral graph

    Symmetry group

    | cuboctahedron | icosidodecahedron symmetry group | octahedral group | icosahedral group

    Common properties

    amphichiral | Archimedean | canonical | convex | equilateral | quasiregular | rigid | simple | uniform

    Associated people

    Archimedes

    Archimedes

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