Polytope Information:
========================
Num_Vertices:=64;
Order_of_Aut_Grp:=21504;
Num_Facet_Orbits:=67;
Facet_Incidences:=[ 14, 15, 16, 17, 19, 22, 28, 32 ];
Cos_squared_of_deep hole:=1/14;
Deep_hole_facet_orbits:=[ 16 ];
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Facet Orbit Nr.1:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=7/50;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 28, 29, 30, 41, 58, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet_Gram:=
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Facet Orbit Nr.2:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=121/889;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 29, 30, 31, 41, 53, 58, 61, 62, 64 ];
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Facet_Gram:=
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Facet Orbit Nr.3:
========================
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Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
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Facet Orbit Nr.4:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=8;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=64/441;
Vertices_in_Facet:=[ 1, 6, 15, 18, 19, 28, 29, 30, 31, 53, 58, 62, 63, 64 ];
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Facet Orbit Nr.5:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=289/1981;
Vertices_in_Facet:=[ 1, 6, 9, 15, 18, 19, 28, 29, 30, 31, 53, 58, 63, 64 ];
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Facet Orbit Nr.6:
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Facet Orbit Nr.7:
========================
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Facet Orbit Nr.8:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=7/47;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 28, 29, 30, 31, 53, 58, 63, 64 ];
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Facet Orbit Nr.10:
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Facet Orbit Nr.11:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=27/182;
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Facet Orbit Nr.12:
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Facet Orbit Nr.13:
========================
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Facet Orbit Nr.14:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=4/29;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 28, 29, 30, 31, 53, 58, 61, 62, 64 ];
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Facet Orbit Nr.15:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=81/574;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 28, 29, 41, 53, 58, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet_Normal:=[ 1, -1/3, 1/9, -1/3, -1/3, 1, 1, -5/9, 1, 1/3, -1/3, -1/3, 
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Facet_Gram:=
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Facet Orbit Nr.16:
========================
Num_Vertices:=32;
Order_of_Auto_Grp:=2304;
Order_of_Stab_in_Grp_of_Poly:=768;
Orbit_Size:=28;
Cos_squared_of_corr_hole:=1/14;
Vertices_in_Facet:=[ 1, 3, 5, 6, 7, 9, 12, 15, 19, 22, 26, 28, 30, 31, 33, 
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Facet Orbit Nr.17:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=1;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=13/98;
Vertices_in_Facet:=[ 1, 6, 7, 9, 10, 15, 28, 29, 30, 41, 58, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet Orbit Nr.18:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=125/889;
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Facet_Gram:=
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Facet Orbit Nr.19:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=25/182;
Vertices_in_Facet:=[ 1, 6, 7, 15, 19, 28, 29, 30, 33, 41, 55, 58, 61, 62, 64 
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Facet_Gram:=
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      1/157, 1/157, 1/157, 1/157, 1, 1/157 ], 
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      1/157, 1/157, -103/157, 1/157, 1 ] ];


Facet Orbit Nr.20:
========================
Num_Vertices:=28;
Order_of_Auto_Grp:=168;
Order_of_Stab_in_Grp_of_Poly:=168;
Orbit_Size:=128;
Cos_squared_of_corr_hole:=4/49;
Vertices_in_Facet:=[ 1, 2, 6, 9, 10, 14, 15, 18, 19, 20, 23, 27, 28, 29, 30, 
  33, 38, 41, 44, 51, 53, 57, 58, 59, 60, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet Orbit Nr.21:
========================
Num_Vertices:=17;
Order_of_Auto_Grp:=12;
Order_of_Stab_in_Grp_of_Poly:=6;
Orbit_Size:=3584;
Cos_squared_of_corr_hole:=9/70;
Vertices_in_Facet:=[ 1, 7, 9, 15, 19, 28, 29, 30, 31, 41, 45, 53, 55, 58, 61, 
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Vertices_of_Repr:=
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Facet Orbit Nr.22:
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Facet Orbit Nr.23:
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Facet Orbit Nr.24:
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Facet_Gram:=
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Facet Orbit Nr.25:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=32;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=1/7;
Vertices_in_Facet:=[ 1, 6, 9, 15, 18, 19, 22, 28, 29, 30, 31, 53, 62, 63, 64 
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Vertices_of_Repr:=
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Facet Orbit Nr.26:
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Facet Orbit Nr.27:
========================
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Facet Orbit Nr.28:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=5/34;
Vertices_in_Facet:=[ 6, 9, 15, 18, 19, 28, 29, 30, 31, 40, 53, 58, 62, 64 ];
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Facet Orbit Nr.29:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=64/469;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 18, 19, 28, 29, 30, 31, 58, 63, 64 ];
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Facet Orbit Nr.30:
========================
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Facet Orbit Nr.31:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=48;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=7/46;
Vertices_in_Facet:=[ 1, 6, 9, 15, 18, 19, 28, 30, 53, 57, 58, 62, 63, 64 ];
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Facet Orbit Nr.32:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=8;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=1/7;
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Facet Orbit Nr.33:
========================
Num_Vertices:=22;
Order_of_Auto_Grp:=42;
Order_of_Stab_in_Grp_of_Poly:=21;
Orbit_Size:=1024;
Cos_squared_of_corr_hole:=1/10;
Vertices_in_Facet:=[ 1, 3, 6, 7, 8, 9, 10, 11, 15, 18, 22, 28, 29, 30, 31, 
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Facet_Gram:=
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Facet Orbit Nr.34:
========================
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Order_of_Auto_Grp:=16;
Order_of_Stab_in_Grp_of_Poly:=2;
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Facet Orbit Nr.35:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=32;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=18/119;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 19, 22, 28, 29, 30, 31, 53, 63, 64 ];
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Facet Orbit Nr.36:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=32;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=50/329;
Vertices_in_Facet:=[ 1, 6, 7, 9, 15, 18, 19, 22, 28, 29, 31, 53, 62, 64 ];
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Facet Orbit Nr.37:
========================
Num_Vertices:=15;
Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=32/245;
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Facet Orbit Nr.38:
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Facet Orbit Nr.39:
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Facet Orbit Nr.40:
========================
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Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
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Facet Orbit Nr.41:
========================
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Facet Orbit Nr.42:
========================
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Facet Orbit Nr.43:
========================
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Order_of_Auto_Grp:=1;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=529/3962;
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Facet Orbit Nr.45:
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Facet Orbit Nr.46:
========================
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Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
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Facet Orbit Nr.48:
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Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=7/50;
Vertices_in_Facet:=[ 6, 7, 9, 10, 15, 28, 29, 30, 41, 47, 58, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet_Normal:=[ 5/7, -1/7, 1/7, -1/7, -3/7, 1, 1, -1/7, 1, 1, 3/7, -5/7, -1, 
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  -1/7, 1/7, 1, 1, 1/7, 1 ];
Facet_Gram:=
[ [ 1, 1/301, 1/301, 1/301, 1/301, -99/301, 1/301, 1/301, 1/301, 1/301, 
      -199/301, 1/301, 1/301, 1/301 ], 
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  [ 1/301, 1/301, 1/301, 1/301, -99/301, 1/301, 1/301, 1/301, 1/301, 1/301, 
      1/301, -199/301, 1/301, 1 ] ];


Facet Orbit Nr.49:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=4;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=21/146;
Vertices_in_Facet:=[ 6, 7, 9, 15, 28, 29, 30, 31, 41, 47, 58, 61, 62, 64 ];
Vertices_of_Repr:=
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Facet Orbit Nr.50:
========================
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Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=99/686;
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Facet Orbit Nr.51:
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Facet Orbit Nr.52:
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Facet Orbit Nr.53:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=2;
Orbit_Size:=10752;
Cos_squared_of_corr_hole:=121/833;
Vertices_in_Facet:=[ 6, 9, 15, 18, 19, 23, 28, 29, 30, 31, 40, 53, 58, 62 ];
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Facet_Gram:=
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Facet Orbit Nr.54:
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Facet Orbit Nr.55:
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Facet Orbit Nr.56:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=7680;
Order_of_Stab_in_Grp_of_Poly:=4;
Orbit_Size:=5376;
Cos_squared_of_corr_hole:=8/49;
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Facet Orbit Nr.59:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=1;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
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Facet Orbit Nr.61:
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Facet Orbit Nr.62:
========================
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Order_of_Auto_Grp:=2;
Order_of_Stab_in_Grp_of_Poly:=1;
Orbit_Size:=21504;
Cos_squared_of_corr_hole:=13/98;
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Facet Orbit Nr.64:
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Facet Orbit Nr.65:
========================
Num_Vertices:=14;
Order_of_Auto_Grp:=24;
Order_of_Stab_in_Grp_of_Poly:=6;
Orbit_Size:=3584;
Cos_squared_of_corr_hole:=1/7;
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Facet Orbit Nr.66:
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Facet Orbit Nr.67:
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Facet_Gram:=
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