Polytope of Type {2,2,7}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,7}*56
if this polytope has a name.
Group : SmallGroup(56,12)
Rank : 4
Schlafli Type : {2,2,7}
Number of vertices, edges, etc : 2, 2, 7, 7
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,7,2} of size 112
   {2,2,7,14} of size 784
   {2,2,7,3} of size 1344
   {2,2,7,4} of size 1344
   {2,2,7,6} of size 1344
   {2,2,7,7} of size 1344
   {2,2,7,8} of size 1344
   {2,2,7,8} of size 1344
Vertex Figure Of :
   {2,2,2,7} of size 112
   {3,2,2,7} of size 168
   {4,2,2,7} of size 224
   {5,2,2,7} of size 280
   {6,2,2,7} of size 336
   {7,2,2,7} of size 392
   {8,2,2,7} of size 448
   {9,2,2,7} of size 504
   {10,2,2,7} of size 560
   {11,2,2,7} of size 616
   {12,2,2,7} of size 672
   {13,2,2,7} of size 728
   {14,2,2,7} of size 784
   {15,2,2,7} of size 840
   {16,2,2,7} of size 896
   {17,2,2,7} of size 952
   {18,2,2,7} of size 1008
   {19,2,2,7} of size 1064
   {20,2,2,7} of size 1120
   {21,2,2,7} of size 1176
   {22,2,2,7} of size 1232
   {23,2,2,7} of size 1288
   {24,2,2,7} of size 1344
   {25,2,2,7} of size 1400
   {26,2,2,7} of size 1456
   {27,2,2,7} of size 1512
   {28,2,2,7} of size 1568
   {29,2,2,7} of size 1624
   {30,2,2,7} of size 1680
   {31,2,2,7} of size 1736
   {32,2,2,7} of size 1792
   {33,2,2,7} of size 1848
   {34,2,2,7} of size 1904
   {35,2,2,7} of size 1960
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,7}*112, {2,2,14}*112
   3-fold covers : {6,2,7}*168, {2,2,21}*168
   4-fold covers : {8,2,7}*224, {2,2,28}*224, {2,4,14}*224, {4,2,14}*224
   5-fold covers : {10,2,7}*280, {2,2,35}*280
   6-fold covers : {12,2,7}*336, {4,2,21}*336, {2,6,14}*336, {6,2,14}*336, {2,2,42}*336
   7-fold covers : {2,2,49}*392, {2,14,7}*392, {14,2,7}*392
   8-fold covers : {16,2,7}*448, {2,4,28}*448, {4,2,28}*448, {4,4,14}*448, {2,2,56}*448, {2,8,14}*448, {8,2,14}*448
   9-fold covers : {18,2,7}*504, {2,2,63}*504, {2,6,21}*504, {6,2,21}*504
   10-fold covers : {20,2,7}*560, {4,2,35}*560, {2,10,14}*560, {10,2,14}*560, {2,2,70}*560
   11-fold covers : {22,2,7}*616, {2,2,77}*616
   12-fold covers : {24,2,7}*672, {8,2,21}*672, {2,12,14}*672, {12,2,14}*672, {2,6,28}*672a, {6,2,28}*672, {4,6,14}*672a, {6,4,14}*672, {2,2,84}*672, {2,4,42}*672a, {4,2,42}*672, {2,6,21}*672, {2,4,21}*672
   13-fold covers : {26,2,7}*728, {2,2,91}*728
   14-fold covers : {4,2,49}*784, {2,2,98}*784, {28,2,7}*784, {4,14,7}*784, {2,14,14}*784a, {2,14,14}*784b, {14,2,14}*784
   15-fold covers : {30,2,7}*840, {10,2,21}*840, {6,2,35}*840, {2,2,105}*840
   16-fold covers : {32,2,7}*896, {4,4,28}*896, {2,4,56}*896a, {2,4,28}*896, {2,4,56}*896b, {2,8,28}*896a, {2,8,28}*896b, {4,2,56}*896, {8,2,28}*896, {4,8,14}*896a, {8,4,14}*896a, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896, {2,2,112}*896, {2,16,14}*896, {16,2,14}*896
   17-fold covers : {34,2,7}*952, {2,2,119}*952
   18-fold covers : {36,2,7}*1008, {4,2,63}*1008, {2,18,14}*1008, {18,2,14}*1008, {2,2,126}*1008, {12,2,21}*1008, {4,6,21}*1008, {6,6,14}*1008a, {6,6,14}*1008b, {6,6,14}*1008c, {2,6,42}*1008a, {2,6,42}*1008b, {2,6,42}*1008c, {6,2,42}*1008
   19-fold covers : {38,2,7}*1064, {2,2,133}*1064
   20-fold covers : {40,2,7}*1120, {8,2,35}*1120, {2,20,14}*1120, {20,2,14}*1120, {2,10,28}*1120, {10,2,28}*1120, {4,10,14}*1120, {10,4,14}*1120, {2,2,140}*1120, {2,4,70}*1120, {4,2,70}*1120
   21-fold covers : {6,2,49}*1176, {2,2,147}*1176, {6,14,7}*1176, {2,14,21}*1176, {14,2,21}*1176, {42,2,7}*1176
   22-fold covers : {44,2,7}*1232, {4,2,77}*1232, {2,22,14}*1232, {22,2,14}*1232, {2,2,154}*1232
   23-fold covers : {46,2,7}*1288, {2,2,161}*1288
   24-fold covers : {48,2,7}*1344, {16,2,21}*1344, {12,2,28}*1344, {4,6,28}*1344a, {4,12,14}*1344a, {12,4,14}*1344, {6,4,28}*1344, {2,24,14}*1344, {24,2,14}*1344, {2,6,56}*1344, {6,2,56}*1344, {6,8,14}*1344, {8,6,14}*1344, {2,12,28}*1344, {2,4,84}*1344a, {4,2,84}*1344, {4,4,42}*1344, {2,2,168}*1344, {2,8,42}*1344, {8,2,42}*1344, {2,12,21}*1344, {4,6,21}*1344, {4,4,21}*1344b, {2,8,21}*1344, {4,6,14}*1344, {6,4,14}*1344, {6,6,14}*1344, {2,6,28}*1344, {2,6,42}*1344, {2,4,42}*1344
   25-fold covers : {50,2,7}*1400, {2,2,175}*1400, {2,10,35}*1400, {10,2,35}*1400
   26-fold covers : {52,2,7}*1456, {4,2,91}*1456, {2,26,14}*1456, {26,2,14}*1456, {2,2,182}*1456
   27-fold covers : {54,2,7}*1512, {2,2,189}*1512, {2,6,63}*1512, {6,2,63}*1512, {18,2,21}*1512, {6,6,21}*1512a, {2,6,21}*1512, {6,6,21}*1512b
   28-fold covers : {8,2,49}*1568, {2,2,196}*1568, {2,4,98}*1568, {4,2,98}*1568, {56,2,7}*1568, {8,14,7}*1568, {2,14,28}*1568a, {2,14,28}*1568b, {2,28,14}*1568a, {14,2,28}*1568, {28,2,14}*1568, {4,14,14}*1568a, {14,4,14}*1568, {4,14,14}*1568c, {2,28,14}*1568c
   29-fold covers : {58,2,7}*1624, {2,2,203}*1624
   30-fold covers : {60,2,7}*1680, {20,2,21}*1680, {12,2,35}*1680, {4,2,105}*1680, {6,10,14}*1680, {10,6,14}*1680, {2,30,14}*1680, {30,2,14}*1680, {2,10,42}*1680, {10,2,42}*1680, {2,6,70}*1680, {6,2,70}*1680, {2,2,210}*1680
   31-fold covers : {62,2,7}*1736, {2,2,217}*1736
   32-fold covers : {64,2,7}*1792, {4,8,14}*1792a, {8,4,14}*1792a, {2,8,28}*1792a, {2,4,56}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {2,8,56}*1792a, {2,8,56}*1792b, {2,8,56}*1792c, {8,8,14}*1792d, {2,8,56}*1792d, {8,2,56}*1792, {8,4,28}*1792a, {4,4,56}*1792a, {8,4,28}*1792b, {4,4,56}*1792b, {4,8,28}*1792a, {4,4,28}*1792a, {4,4,28}*1792b, {4,8,28}*1792b, {4,8,28}*1792c, {4,8,28}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {2,16,28}*1792a, {2,4,112}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {2,16,28}*1792b, {2,4,112}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {2,4,28}*1792, {2,4,56}*1792b, {2,8,28}*1792b, {16,2,28}*1792, {4,2,112}*1792, {2,32,14}*1792, {32,2,14}*1792, {2,2,224}*1792
   33-fold covers : {22,2,21}*1848, {66,2,7}*1848, {6,2,77}*1848, {2,2,231}*1848
   34-fold covers : {68,2,7}*1904, {4,2,119}*1904, {2,34,14}*1904, {34,2,14}*1904, {2,2,238}*1904
   35-fold covers : {10,2,49}*1960, {2,2,245}*1960, {10,14,7}*1960, {2,14,35}*1960, {14,2,35}*1960, {70,2,7}*1960
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11);;
s3 := ( 5, 6)( 7, 8)( 9,10);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(1,2);
s1 := Sym(11)!(3,4);
s2 := Sym(11)!( 6, 7)( 8, 9)(10,11);
s3 := Sym(11)!( 5, 6)( 7, 8)( 9,10);
poly := sub<Sym(11)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope