Polytope of Type {7,2,2}

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

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

Permutation Representation (Magma) :

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

to this polytope