Noble Polyhedra: Icosahedral 10 colour arrangements

Notes:  In all cases one representative set of faces 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.

Structurally Excess Minimum Injective Face-Colourings of Noble Polyhedra with 'I' (Chiral Icosahedral) Symmetry

A 5-colour or 6-colour arrangement is not possible for these polyhedra due to topological and geometric adjacency constraints.  When a maximal set of vertex-disjoint faces possesses 3-fold dihedral symmetry (D3), the faces partition into orbits of 6, requiring a 10-colour arrangement.

 
I-5-60-150-60-W7733-(rD-1.2)_I_10col_D3
rD-1.2
Hull: Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7733
 I-5-60-150-60-W5317-(rD-3.2)_I_10col_D3
rD-3.2
Hull: Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 5317
I-5-60-150-60-W4530-(rD-6.1)_I_10col_D3
rD-6.1
Hull: Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 4530
 I-5-60-150-60-W7070-(rD-8.2)_I_10col_D3
rD-8.2
Hull: Rhombicosidodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7070
I-5-60-150-60-W6474-(sD-1.1)_I_10col_D3
sD-1.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 6474
 I-5-60-150-60-W7304-(sD-10.1)_I_10col_D3
sD-10.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7304
I-5-60-150-60-W8293-(sD-11.1)_I_10col_D3
sD-11.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8293
 I-5-60-150-60-W8871-(sD-13.1)_I_10col_D3
sD-13.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8871
I-5-60-150-60-W7040-(sD-16.1)_I_10col_D3
sD-16.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7040
 I-5-60-150-60-W7962-(sD-17.1)_I_10col_D3
sD-17.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7962
I-5-60-150-60-W7230-(sD-18.1)_I_10col_D3
sD-18.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7230
 I-5-60-150-60-W8036-(sD-2.1)_I_10col_D3
sD-2.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8036
I-5-60-150-60-W7912-(sD-20.1)_I_10col_D3
sD-20.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7912
 I-5-60-150-60-W8087-(sD-21.1)_I_10col_D3
sD-21.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8087
I-5-60-150-60-W3891-(sD-24.1)_I_10col_D3
sD-24.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 3891
 I-5-60-150-60-W7268-(sD-25.1)_I_10col_D3
sD-25.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7268
I-5-60-150-60-W3900-(sD-25.2)_I_10col_D3
sD-25.2
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 3900
 I-5-60-150-60-W3422-(sD-26.1)_I_10col_D3
sD-26.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 3422
I-5-60-150-60-W5706-(sD-27.1)_I_10col_D3
sD-27.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 5706
 I-5-60-150-60-W8278-(sD-28.1)_I_10col_D3
sD-28.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8278
I-5-60-150-60-W6114-(sD-29.1)_I_10col_D3
sD-29.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 6114
 I-5-60-150-60-W7999-(sD-3.1)_I_10col_D3
sD-3.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 7999
I-5-60-150-60-W4126-(sD-5.1)_I_10col_D3
sD-5.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 4126
 I-5-60-150-60-W3667-(sD-5.2)_I_10col_D3
sD-5.2
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 3667
I-5-60-150-60-W6967-(sD-7.1)_I_10col_D3
sD-7.1
Hull: Snub Dodecahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 6967
 I-5-60-150-60-W8135-(tI-1.2)_I_10col_D3
tI-1.2
Hull: Truncated Icosahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8135
I-5-60-150-60-W8049-(tI-7.1)_I_10col_D3
tI-7.1
Hull: Truncated Icosahedron
Gonality / Valence: 5 / 5
V-E-F: 60-150-60
Genus / Wiener Index: 16 / 8049

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