18 distinct colourings are listed here:
"0"
"1"
"2"
"3"
"4"
"5"
"6"
"7"
"8"
"9"
"10"
"11"
"12"
"13"
"14"
"15"
"16"
"17"
The first seven listed above have mirror symmetry, the last eleven are chiral.
Some relations between them are indicated in this image, in which the letters "MR" refer to their index numbers in this paper.
All rotations of the icosahedron preserve the edge-colouring while permuting the colours.
Swap yellow and black for circuit (1,7,2,9,3,5), shape M, to find "1".
| all colours | S |
| all colour pairs | M |
Isomorphic to MR29.
Swap yellow and black for circuit (1,7,2,9,3,5), shape M, to find "0".
Swap red and green for circuit (1,2,3,4,5,6), shape M, to find "2".
| R G B | S |
| Y | D |
| K | L |
| RG RB GB YK | M |
| RY GY BY | G- |
| RK GK BK | G+ |
Isomorphic to MR28.
Swap red and green for circuit (1,2,3,4,5,6), shape M, to find "1".
Swap red and black for circuit (1,6,12,7), shape O, to find "3".
| R Y | D |
| G K | L |
| B | S |
| RG YK | M |
| RB BY | G- |
| RY | N- |
| RK GY | O |
| GB BK | G+ |
| GK | N+ |
Isomorphic to MR26.
Swap red and black for circuit (1,6,12,7), shape O, to find "2".
Swap green and yellow for circuit (3,4,10,9), shape O, to find "4".
| R | 7 |
| G | L |
| B | S |
| Y | D |
| K | 3 |
| RG | H- |
| RB | E- |
| RY | J- |
| RK GY | O |
| GB | G+ |
| GK | J+ |
| BY | G- |
| BK | E+ |
| YK | H+ |
Isomorphic to MR22.
| R | 7 |
| G | 3 |
| B | S |
| Y | 7 |
| K | 3 |
| RG YK | P |
| RB BY | E- |
| RY | N+ |
| RK GY | O |
| GB BK | E+ |
| GK | N- |
Isomorphic to MR25.
Swap red and green for circuit (1,2,3,9,8,7), shape P, to find "4".
Swap yellow and black for circuit (1,5,3,4,11,6), shape P, to find "6".
| R | 5 |
| G | 5 |
| B | S |
| Y | 7 |
| K | 3 |
| RG YK | P |
| RB | L- |
| RY | Q+ |
| RK | Q- |
| GB | L+ |
| GY | Q+ |
| GK | Q- |
| BY | E- |
| BK | E+ |
Isomorphic to MR18.
Swap yellow and black for circuit (1,5,3,4,11,6), shape P, to find "5".
| R | 5 |
| G | 5 |
| B | S |
| Y | 5 |
| K | S |
| RG RY RK GY GK YK | P |
| BK BK | L- |
| GB BY | L+ |
Isomorphic to MR20.
Swap green and black for circuit (1,2,9,3,5,6), shape N, to find "4".
| R | 7 |
| G | D |
| B | S |
| Y | 7 |
| K | D |
| RG RK | τ+ |
| RB BY | E- |
| RY | N+ |
| GB BK | G- |
| GY YK | π+ |
| GK | N- |
Isomorphic to MR24 and (with reflection) to MR27.
Swap yellow and black for (1,5,11,6), shape α, to find "12".
| R | 7 |
| G | 1 |
| B | 9 |
| Y | 7 |
| K | 1 |
| RG | T- |
| RB | S- |
| RY | V+ |
| RK | ι- |
| GB | W+ |
| GY | μ- |
| GK | T- |
| BY | N+ |
| BK | ζ |
| YK | α+ |
Isomorphic to MR6 and (with reflection) to MR10.
| R | D |
| G | 1 |
| B | 9 |
| Y | D |
| K | 9 |
| RG | Y+ |
| RB | α- |
| RY | N- |
| RK | X- |
| GB | W+ |
| GY | Y+ |
| GK | W- |
| BY | β- |
| BK | σ- |
| YK | X- |
Isomorphic to MR7 and (with reflecction) to MR21.
Swap yellow and black for (1,5,11,6), shape α, to find "11"
Swap red and green for (2,3,1,7,8,9), shape T, to find "12".
| R G B | 9 |
| Y | D |
| K | 5 |
| RG RB GB | T- |
| RY GY BY | β- |
| RK GK BK | δ+ |
| YK | α+ |
Isomorphic to MR16 and (with reflecction) to MR19.
Swap yellow and black for (1,5,11,6), shape α, to find "10".
Swap red and yellow for (4,5,11,10), shape V, to find "13".
| R G B | 9 |
| Y | 7 |
| K | 1 |
| RG RB GB | T- |
| RY BY | V- |
| RK BK | ζ |
| GY | S- |
| GK | W- |
| YK | α+ |
Isomorphic to MR15 and (with reflecction) to MR12.
Swap yellow and black for (1,5,11,6), shape α, to find "8".
Swap red and black for (1,6,12,7), shape X, to find "9".
Swap red and green for (2,3,1,7,8,9), shape T, to find "10".
Swap green and black for (1,3,4,11,5,6), shape θ, to find "14".
| R | 7 |
| G | 1 |
| B | 9 |
| Y | D |
| K | 5 |
| RG | T- |
| RB | S- |
| RY | J- |
| RK | X- |
| GB | W+ |
| GY | Y+ |
| GK | θ+ |
| BY | β- |
| BK | δ+ |
| YK | α+ |
Isomorphic to MR5 and (with reflecction) to MR17.
Swap red and yellow for (4,5,11,10), shape V, to find "11".
| R Y | 3 |
| G B | 9 |
| K | 1 |
| RG | T+ |
| RB | ι+ |
| RY | V- |
| RK | S+ |
| GB | T- |
| GY | μ+ |
| GK | W- |
| BY | α- |
| BK | ζ |
| YK | V+ |
Isomorphic to MR13 and (with reflecction) to MR8.
Swap green and black for (1,3,4,11,5,6), shape θ, to find "12".
Swap yellow and black for (2,7,12,8), shape ϡ, to find "15".
| R | 7 |
| G | 3 |
| B | 9 |
| Y | D |
| K | 3 |
| RG | φ+ |
| RB | S- |
| RY | J- |
| RK | φ+ |
| GB | ι+ |
| GY | ϡ+ |
| GK | θ+ |
| BY | β- |
| BK | ι+ |
| YK | ϡ- |
Isomorphic to MR14 and (with reflecction) to MR23.
Swap yellow and black for (2,7,12,8), shape ϡ, to find "14".
Swap blue and black for (1,2,7,6,5,3), shape T, to find "16".
| R | 7 |
| G | 3 |
| B | 9 |
| Y | 7 |
| K | 9 |
| RG | φ+ |
| RB | S- |
| RY | V+ |
| RK | V- |
| GB | ι+ |
| GY | ζ |
| GK | T+ |
| BY | V- |
| BK | T- |
| YK | ϡ- |
Isomorphic to MR4 and (with reflecction) to MR2.
Swap blue and black for (1,2,7,6,5,3), shape T, to find "15".
Swap green and black for (3,4,11,5), shape V, to find "17".
| R | 7 |
| G | 3 |
| B | 7 |
| Y | 7 |
| K | 1 |
| RG | φ+ |
| RB | V+ |
| RY | V+ |
| RK | μ- |
| GB | φ- |
| GY | ζ |
| GK | V+ |
| BY | π+ |
| BK | T- |
| YK | ι- |
Isomorphic to MR3 and (with reflecction) to MR1.
Rotations of the icosahedron about the axis through the vertices marked in grey preserve the edge-colouring while permuting the colours.
Swap green and black for (3,4,11,5), shape V, to find "16".
| all colours | 7 |
| RG RK GY BY BK | π+ |
| RB RY GB GK YK | V+ |
Isomorphic to MR9 and (with reflecction) to MR11.
