I still like my notation better. It's easier to program.
F4 [2]^4
F6 [3]^6
F8 [3,-3]^4
F10 [3,-3, Infinity]^3
F14 [5,-5]^7
F16 [5,-5]^8
F18 [5,7,-7,7,-7,-5]^3 or [5,7,-7;-]^3 in the "antipalindromic" notation
F20A [10, 7, 4, -4, -7, 10, -4, 7, -7, 4]^2
F20B [-9, 5, -5, 9]^5 or [-9,5;-]^5 in the antipalindromic notation
F24 [5,-9,7,-7,9,-5]^4, or [5,-9,7;-] in antipalindromic
F26 [7,-7]^13
F28 No LCF representation
F30 [-7, 9, 13, -13, -9, 7]^5, or [-7,9,13;-]^5
F32 [-5, 13, -13, 5]^8, or [-5,13;-]^2
F38 [15,-15]^19
F40 [15,9,-9,-15]^10 , or [15,9;-]^10
F42 [5, -17, 17, 13,-13,-5]^7
F48 [-7, 9, 19, -19, -9, 7]^8, or [-7,9,19;-]^8
F50 ???
F54 gapgraph[{0, 11, 0, 11, 13, 0}, 9];
F56A gapgraph[{0, 0, 11, 13}, 14]
F56B ???
F56C ???
F60 [12,-17,-12,25,17,-26,-9,9,-25,26]^6
F90 [17, -9, 37, -37, 9, -17]^15
{{62, 1}, {64, 1}, {72, 1}, {74, 1}, {78, 1}, {80, 1},
{84, 1}, {86, 1}, {90, 1}, {96, 2}, {98, 2}, {100, 2},
{102, 1}, {104, 1}, {108, 1}, {110, 1}, {112, 3}, {114, 1},
{120, 2}, {122, 1}, {126, 1}, {128, 2}, {134, 1}, {144, 2},
{146, 1}, {150, 1}, {152, 1}, {158, 1}, {162, 3}, {168, 6},
{182, 4}, {186, 1}, {192, 3}, {194, 1}}
First, find a path of length 7. How many colors do you use?
Next, find a path of length 8. How many colors do you use?
Next, find a path of length 9. Did you use one color three times?
Pick a word you don't like. Find a path that goes through all of the
other words.
Have a friend start a different word. Both of you travel length 14
paths back to the starting words, without reusing any words.
It's called the LCF notation. In it, the cube graph is [3,-3]^4.
The 1981 book Zero-Symmetric Graphs covers the notation
in detail. HSM Coxeter, Roberto Frucht, David Powers.
The book was written at Ronald Foster's urging.
F4 [2,-2]^2
F6 [3,-3]^3
F8 [3,-3]^4
F10 [3,-3, Infinity]^3
F14 [5,-5]^7
F16 [5,-5]^8
F18 [5,7,-7,7,-7,-5]^3 or [5,7,-7;-]^3 in the "antipalindromic" notation
F20A [10, 7, 4, -4, -7, -10, -4, 7, -7, 4]^2
F20B [-9, 5, -5, 9]^5 or [-9,5;-]^5 in the antipalindromic notation