Polytope of Type {2,7,2}

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

s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := (3,4)(5,6)(7,8);;
s3 := (10,11);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope