Dodecahedral symmetry

From Polytope Wiki
Jump to navigation Jump to search
Dodecahedral symmetry
Rank3
SpaceSpherical
Order120
Info
Coxeter diagram
Elements
Axes6 × (I2(10)×A1)/2, 10 × (G2×A1)/2, 15 × K3
Related polytopes
OmnitruncateGreat rhombicosidodecahedron

Dodecahedral symmetry, also known as icosahedral symmetry, doic symmetry, and notated as H3, is a 3D spherical Coxeter group. It is the symmetry group of the dodecahedron and icosahedron.

Subgroups[edit | edit source]

Convex polytopes with H3 symmetry[edit | edit source]

Wythoffians with H3 symmetry[edit | edit source]

o5/2o3o3*a truncations
Name OBSA CD diagram Picture
Small ditrigonary icosidodecahedron sidtid x5/2o3o3*a ()
(degenerate, double cover of id) x5/2x3o3*a ()
(degenerate, double cover of ike) o5/2o3x3*a ()
Small icosicosidodecahedron siid x5/2o3x3*a ()
(degenerate, double cover of ti) x5/2x3x3*a ()
Small snub icosicosidodecahedron seside s5/2s3s3*a ()
o5/3o3o5*a truncations
Name OBSA CD diagram Picture
Ditrigonary dodecadodecahedron ditdid
Small complex icosidodecahedron (degenerate, ike+gad) cid
Great complex icosidodecahedron (degenerate, sissid+gike) gacid
Icosidodecadodecahedron ided
Small ditrigonal dodecicosidodecahedron sidditdid
Great ditrigonal dodecicosidodecahedron gidditdid
Icosidodecatruncated icosidodecahedron idtid
Snub icosidodecadodecahedron sided
o5/3o5/2o3*a truncations
Name OBSA CD diagram Picture
Great complex icosidodecahedron (degenerate, sissid+gike) gacid x5/3o5/2o3*a ()
Great dodecicosidodecahedron gaddid x5/3x5/2o3*a ()
(degenerate, double cover of gissid) o5/3x5/2o3*a ()
(degenerate, ditdid+gidtid) o5/3x5/2x3*a ()
Great complex icosidodecahedron (degenerate, sissid+gike) gacid o5/3o5/2x3*a ()
(degenerate, double cover of sidhei) x5/3o5/2x3*a ()
(degenerate, giddy+12(10/2)) x5/3x5/2x3*a ()
Great snub dodecicosidodecahedron gisdid s5/3s5/2s2*a ()