For each orbit of faces of codimension k we give a canonical representative face f_i.
The face fk_i is defined by a set of k inequalities of rank k satisfied with equality.
A triangular inequality Tr of met_n is represented by a {-1,0,1}-valued vector V of
length n with 3 nonzero entries with: Tr_ij = V_i x V_j. The left hand side of Tr
is 2 if V is a {0,1}-valued vector and 0 otherwise.
+++++ remark ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
the set of all inequalities satisfied with equality by f_i might be larger than k
but we show only k facets. This way the codimension is directly readable and the
presentation is homogeneous)
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
-------------- canonical representatives --------------------------
f4_1
1 1 1 0
1 1 0 1
1 0 1 1
0 1 1 1
f4_2
1 1 1 0 0
1 1 0 1 0
1 0 1 1 0
1 1 0 0 1
f4_3
1 1 1 0 0
1 1 0 1 0
1 0 1 1 0
0 1 1 0 1
f4_4
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 1 0 0
1 0 0 0 1 1
f4_5
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 1 0 0
0 1 0 0 1 1
f4_6
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 1 1 0 0 0
0 0 0 0 1 1 1
f4_7
1 1 1 0 0
1 1 0 1 0
1 0 -1 1 0
1 1 0 0 1
f4_8
1 1 1 0 0 0
1 1 0 1 0 0
1 0 -1 1 0 0
1 0 0 0 1 1
f4_9
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 -1 1 0 0 0
0 0 0 0 1 1 1
f4_10
1 1 1 0 0
1 1 0 1 0
1 1 0 0 1
0 0 1 1 1
f4_11
1 1 1 0 0
1 1 0 1 0
1 1 0 0 1
0 0 -1 1 1
f4_12
1 1 1 0 0 0
1 1 0 1 0 0
1 1 0 0 1 0
1 1 0 0 0 1
f4_13
1 1 1 0 0 0
1 1 0 1 0 0
1 1 0 0 1 0
1 0 1 0 0 1
f4_14
1 1 1 0 0 0
1 1 0 1 0 0
1 1 0 0 1 0
0 0 1 1 0 1
f4_15
1 1 1 0 0 0
1 1 0 1 0 0
1 1 0 0 1 0
0 0 -1 1 0 1
f4_16
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 1 0 0 1 0 0
1 0 0 0 0 1 1
f4_17
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 1 0 0 1 0 0
0 0 1 0 0 1 1
f4_18
1 1 1 0 0
1 1 0 1 0
1 0 1 0 1
1 0 0 1 1
f4_19
1 1 1 0 0
1 1 0 1 0
1 0 1 0 1
0 1 0 1 1
f4_20
1 1 1 0 0
1 1 0 1 0
1 0 1 0 1
0 1 0 1 -1
f4_21
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
1 0 0 1 0 1
f4_22
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 1 1 0 0 1
f4_23
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 1 0 1 0 1
f4_24
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 1 0 0 1 1
f4_25
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 -1 0 0 1 1
f4_26
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 0 0 1 1 1
f4_27
1 1 1 0 0 0
1 1 0 1 0 0
1 0 1 0 1 0
0 0 0 -1 1 1
f4_28
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 1 0 1 0 0
1 0 0 0 0 1 1
f4_29
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 1 0 1 0 0
0 1 0 0 0 1 1
f4_30
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 1 0 1 0 0
0 0 0 1 0 1 1
f4_31
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 1 1 0
1 0 0 0 1 1
f4_32
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 1 1 0
-1 0 0 0 1 1
f4_33
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 1 1 0
0 0 1 1 0 1
f4_34
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 1 1 0
0 0 1 0 1 1
f4_35
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 1 1 0 0
1 0 0 0 0 1 1
f4_36
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 1 1 0 0
0 0 1 0 0 1 1
f4_37
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 1 1 0 0
0 0 0 0 1 1 1
f4_38
1 1 1 0 0 0
1 1 0 1 0 0
0 0 -1 1 1 0
1 0 0 0 1 1
f4_39
1 1 1 0 0 0
1 1 0 1 0 0
0 0 -1 1 1 0
0 0 -1 1 0 1
f4_40
1 1 1 0 0 0
1 1 0 1 0 0
0 0 -1 1 1 0
0 0 -1 0 1 1
f4_41
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 -1 1 1 0 0
1 0 0 0 0 1 1
f4_42
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 -1 1 1 0 0
0 0 1 0 0 1 1
f4_43
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 -1 1 1 0 0
0 0 0 0 1 1 1
f4_44
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
1 0 0 0 1 0 1
f4_45
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
0 1 0 0 1 0 1
f4_46
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
0 -1 0 0 1 0 1
f4_47
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
0 0 1 0 1 0 1
f4_48
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
0 0 -1 0 1 0 1
f4_49
1 1 1 0 0 0 0
1 1 0 1 0 0 0
1 0 0 0 1 1 0
0 0 0 0 1 1 1
f4_50
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 0 1 1
0 0 0 1 1 1
f4_51
1 1 1 0 0 0
1 1 0 1 0 0
0 0 1 0 1 1
0 0 0 -1 1 1
f4_52
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 0 1 1 0
0 0 0 1 1 0 1
f4_53
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 0 1 1 0
0 0 0 -1 1 0 1
f4_54
1 1 1 0 0 0 0
1 1 0 1 0 0 0
0 0 1 0 1 1 0
0 0 0 0 1 1 1
f4_55
1 1 1 0 0 0
1 0 0 1 1 0
0 1 0 1 0 1
0 0 -1 0 1 1
f4_56
1 1 1 0 0 0 0
1 0 0 1 1 0 0
0 1 0 1 0 1 0
1 0 0 0 0 1 1
f4_57
1 1 1 0 0 0 0
1 0 0 1 1 0 0
0 1 0 1 0 1 0
-1 0 0 0 0 1 1
f4_58
1 1 1 0 0 0 0
1 0 0 1 1 0 0
0 1 0 1 0 1 0
0 0 1 0 1 0 1
f4_59
1 1 1 0 0 0 0
1 0 0 1 1 0 0
0 1 0 1 0 1 0
0 0 -1 0 1 0 1
f4_60
1 1 1 0 0 0
1 0 0 1 1 0
0 -1 0 1 0 1
0 0 1 0 -1 1
f4_61
1 1 1 0 0 0 0
1 0 0 1 1 0 0
0 -1 0 1 0 1 0
0 0 -1 0 1 0 1