Noble Polyhedra with 'Ih' (icosahedral) symmetry and 5 gonality

Notes:  In all cases one representative face has been highlighted.  This face remains solid through the various displays in the VRML window.  Pressing the 'frame' hud button will display a 'framework' version of the figure, 'hull' will then display the figure with a framework convex hull, 'solid' returns to the initial view.

Ih-5-120-300-120-W20417-(gD-1.1)
gD-1.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 20417
 Ih-5-120-300-120-W36057-(gD-10.1)
gD-10.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 36057
Ih-5-120-300-120-W38187-(gD-11.1)
gD-11.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 38187
 Ih-5-120-300-120-W39933-(gD-12.1)
gD-12.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 39933
Ih-5-120-300-120-W34149-(gD-13.1)
gD-13.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 34149
 Ih-5-120-300-120-W19898-(gD-15.1)
gD-15.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 19898
Ih-5-120-300-120-W22147-(gD-16.1)
gD-16.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 22147
 Ih-5-120-300-120-W38031-(gD-17.1)
gD-17.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 38031
Ih-5-120-300-120-W27614-(gD-18.1)
gD-18.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 27614
 Ih-5-120-300-120-W42968-(gD-19.1)
gD-19.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 42968
Ih-5-120-300-120-W36898-(gD-2.1)
gD-2.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 36898
 Ih-5-120-300-120-W37633-(gD-20.1)
gD-20.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 37633
Ih-5-120-300-120-W21649-(gD-21.1)
gD-21.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 21649
 Ih-5-120-300-120-W22616-(gD-24.1)
gD-24.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 22616
Ih-5-120-300-120-W39559-(gD-25.1)
gD-25.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 39559
 Ih-5-120-300-120-W37310-(gD-26.1)
gD-26.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 37310
Ih-5-120-300-120-W40941-(gD-28.1)
gD-28.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 40941
 Ih-5-120-300-120-W32645-(gD-29.1)
gD-29.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 32645
Ih-5-120-300-120-W25559-(gD-3.1)
gD-3.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 25559
 Ih-5-120-300-120-W40717-(gD-30.1)
gD-30.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 40717
Ih-5-120-300-120-W42498-(gD-31.1)
gD-31.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 42498
 Ih-5-120-300-120-W37851-(gD-32.1)
gD-32.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 37851
Ih-5-120-300-120-W39234-(gD-33.1)
gD-33.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 39234
 Ih-5-120-300-120-W31165-(gD-34.1)
gD-34.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 31165
Ih-5-120-300-120-W27555-(gD-35.1)
gD-35.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 27555
 Ih-5-120-300-120-W26873-(gD-36.1)
gD-36.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 26873
Ih-5-120-300-120-W21788-(gD-37.1)
gD-37.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 21788
 Ih-5-120-300-120-W24357-(gD-38.1)
gD-38.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 24357
Ih-5-120-300-120-W39842-(gD-4.1)
gD-4.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 39842
 Ih-5-120-300-120-W40232-(gD-5.1)
gD-5.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 40232
Ih-5-120-300-120-W40299-(gD-6.1)
gD-6.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 40299
 Ih-5-120-300-120-W41119-(gD-7.1)
gD-7.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 41119
Ih-5-120-300-120-W38480-(gD-8.1)
gD-8.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 38480
 Ih-5-120-300-120-W34141-(gD-9.1)
gD-9.1
Hull: Great Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 120-300-120
Genus / Wiener Index: 31 / 34141


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Footnote.

The Wiener Index is more specifically the Geometric Wiener Index, which is the sum of the shortest paths (along the edges) between any two vertices.  I find it a useful metric as apart from some duplication in the Kepler-Poinsot cases it gives a unique value for every noble polyhedron even when truncated to an integer.  In all cases the polyehdra are scaled to a radius of 1 for this calculation. The topological Wiener Index (which is the sum of the number of edges traversed) is described in wikipedia and in Wolfram Mathworld.  The 'geometric' variant used here is an extension of this using the sum of actual edge lengths.