This is where we share various ways to understand how to graph an Icosahedron.
digraph { layout=circo rankdir=LR overlap=false concentrate=false //bgcolor=lightblue // splines=" " node [shape=box style=rounded] label=" \nIcosohedron 12 Nodes / 30 Edges / 5 Members per Node / 2 Nodes per Member" A -> {1 2 3 4 5} [color=red penwidth=5] B -> {1 6 7 8 9} [color=blue penwidth=5] C -> {2 3 10 11 12} [color=green4 penwidth=5] D -> {4 13 14 15 16} [color=yellow3 penwidth=5] E -> {13 14 17 18 10} [color=orange penwidth=5] F -> {17 18 19 20 21} [color=black penwidth=5] G -> {19 20 21 22 23} [color=purple penwidth=5] H -> {22 23 24 25 26} [color=orange4 penwidth=5] Ii -> {24 25 26 27 28} [color=cyan penwidth=5] J -> {27 28 29 30 5} [color="#7d0b48" penwidth=2] K -> {29 30 6 7 8} [color=gray penwidth=5] L -> {9 15 16 12 11} [color="#746e6e" penwidth=5] A -> {B C D J} [color=black penwidth=5] B -> {A K K K L} [color=black penwidth=5] C -> {A A E L L} [color=black penwidth=5] D -> {A E E L L} [color=black penwidth=5] E -> {D D F F C} [color=black penwidth=5] F -> {E E G G G} [color=black penwidth=5] G -> {F F F H H} [color=black penwidth=5] H -> {G G Ii Ii Ii} [color=black penwidth=5] Ii -> {H H H J J} [color=black penwidth=5] J -> {Ii Ii K K B} [color=black penwidth=5] K -> {J J B B B} [color=black penwidth=5] L -> {B D D C C} [color=black penwidth=5] //node {[shape=circle] A B C D E F G H Ii J K L} A [shape=triangle style=filled color=red] B [shape=triangle style=filled color=red] C [shape=triangle style=filled color=red] D [shape=triangle style=filled color=red] E [shape=triangle style=filled color=red] F [shape=triangle style=filled color=red] G [shape=triangle style=filled color=red] H [shape=triangle style=filled color=red] Ii [shape=triangle style=filled color=red] J [shape=triangle style=filled color=red] K [shape=triangle style=filled color=red] L [shape=triangle style=filled color=red] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 }
digraph { layout=dot rankdir=LR overlap=false concentrate=false //bgcolor=lightblue // splines=" " node [shape=box style=rounded] label=" \nIcosohedron 12 Nodes / 30 Edges / 5 Members per Node / 2 Nodes per Member" A -> {1 2 3 4 5} [color=red penwidth=5] B -> {1 6 7 8 9} [color=blue penwidth=5] C -> {2 3 10 11 12} [color=green4 penwidth=5] D -> {4 13 14 15 16} [color=yellow3 penwidth=5] E -> {13 14 17 18 10} [color=orange penwidth=5] F -> {17 18 19 20 21} [color=black penwidth=5] G -> {19 20 21 22 23} [color=purple penwidth=5] H -> {22 23 24 25 26} [color=orange4 penwidth=5] Ii -> {24 25 26 27 28} [color=cyan penwidth=5] J -> {27 28 29 30 5} [color="#7d0b48" penwidth=2] K -> {29 30 6 7 8} [color=gray penwidth=5] L -> {9 15 16 12 11} [color="#746e6e" penwidth=5] A -> {B C D J} [color=black penwidth=5] B -> {A K K K L} [color=black penwidth=5] C -> {A A E L L} [color=black penwidth=5] D -> {A E E L L} [color=black penwidth=5] E -> {D D F F C} [color=black penwidth=5] F -> {E E G G G} [color=black penwidth=5] G -> {F F F H H} [color=black penwidth=5] H -> {G G Ii Ii Ii} [color=black penwidth=5] Ii -> {H H H J J} [color=black penwidth=5] J -> {Ii Ii K K B} [color=black penwidth=5] K -> {J J B B B} [color=black penwidth=5] L -> {B D D C C} [color=black penwidth=5] //node {[shape=circle] A B C D E F G H Ii J K L} A [shape=triangle style=filled color=red] B [shape=triangle style=filled color=red] C [shape=triangle style=filled color=red] D [shape=triangle style=filled color=red] E [shape=triangle style=filled color=red] F [shape=triangle style=filled color=red] G [shape=triangle style=filled color=red] H [shape=triangle style=filled color=red] Ii [shape=triangle style=filled color=red] J [shape=triangle style=filled color=red] K [shape=triangle style=filled color=red] L [shape=triangle style=filled color=red] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 }
digraph { layout=circo rankdir=LR overlap=false concentrate=false //bgcolor=lightblue // splines=" " node [shape=box style=rounded] label=" \nIcosohedron 12 Nodes / 30 Edges / 5 Members per Node / 2 Nodes per Member" A -> {1 2 3 4 5} [color=red penwidth=5] B -> {1 6 7 8 27} [color=orange penwidth=5] C -> {2 6 29 11 12} [color="#eed200" penwidth=5] D -> {3 7 10 18 14} [color="#fced42" penwidth=5] E -> {4 10 15 16 28} [color=purple penwidth=5] F -> {5 9 11 15 19} [color=lightblue penwidth=5] G -> {13 16 17 14 30} [color=blue penwidth=5] H -> {22 12 24 25 9} [color=green penwidth=5] Ii -> {17 24 19 26 28} [color=brown penwidth=5] J -> {8 13 18 20 21} [color=black penwidth=5] K -> {22 27 23 20 29} [color=gray penwidth=5] L -> {30 21 26 25 23} [color=violet penwidth=5] //node {[shape=circle] A B C D E F G H Ii J K L} A [shape=triangle style=filled color=red] B [shape=triangle style=filled color=orange] C [shape=triangle style=filled color="#eed200"] D [shape=triangle style=filled color="#fced42"] E [shape=triangle style=filled color=purple] F [shape=triangle style=filled color=lightblue] G [shape=triangle style=filled color=blue] H [shape=triangle style=filled color=green] Ii [shape=triangle style=filled color=brown] J [shape=triangle style=filled color=black fontcolor=white] K [shape=triangle style=filled color=grey] L [shape=triangle style=filled color=violet fontcolor=white] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 }