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. 2014 Feb 10;111(8):2920–2925. doi: 10.1073/pnas.1310939111

Table 1.

Equal numbers of DAD equations and independent variables

Group Indices T(h, k) Vertices 20T 6gon angles Vertex types DAD eqs 6gon ID# 6gon type Ind var Tot var
h, 0
1 (1,0) 20 0 1 0 #0 0
4 (2,0) 80 2 2 1 #1 122122 1 1
9 (3,0) 180 4 3 2 #1 122122 1 2
#2 121212 1
16 (4,0) 320 8 5 4 #1 122122 1 4
#2 122122 1
#3 123432 2
49 (7,0) 980 24 12 12 #1 122122 1 12
#2 122122 1
#3 122122 1
#4 123432 2
#5 123456 3
#6 123432 2
#7 123432 2
h = k
3 (1,1) 60 1 1 0 #1 111111 0 0
12 (2,2) 240 4 3 2 #1 122122 1 2
#2 122122 1
#3 111111 0
48 (4,4) 960 21 10 10 #1 122122 1 10
#2 123432 2
#3 122122 1
#4 123456 3
#5 122122 1
#6 122122 1
#7 122122 1
#8 111111 0
h ≠ k
7 (2,1) 140 6 3 3 #1 123456 3 3
13 (3,1) 260 12 5 6 #1 123456 3 6
#2 123456 3
37 (4,3) 740 36 13 18 #1 123456 3 18
#2 123456 3
#3 123456 3
#4 123456 3
#5 123456 3
#6 123456 3

Equal numbers of DAD equations and independent variables.