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Polytope of Type {7,2,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,2,2}*112
if this polytope has a name.
Group : SmallGroup(112,42)
Rank : 5
Schlafli Type : {7,2,2,2}
Number of vertices, edges, etc : 7, 7, 2, 2, 2
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {7,2,2,2,2} of size 224
   {7,2,2,2,3} of size 336
   {7,2,2,2,4} of size 448
   {7,2,2,2,5} of size 560
   {7,2,2,2,6} of size 672
   {7,2,2,2,7} of size 784
   {7,2,2,2,8} of size 896
   {7,2,2,2,9} of size 1008
   {7,2,2,2,10} of size 1120
   {7,2,2,2,11} of size 1232
   {7,2,2,2,12} of size 1344
   {7,2,2,2,13} of size 1456
   {7,2,2,2,14} of size 1568
   {7,2,2,2,15} of size 1680
   {7,2,2,2,16} of size 1792
   {7,2,2,2,17} of size 1904
Vertex Figure Of :
   {2,7,2,2,2} of size 224
   {14,7,2,2,2} of size 1568
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {7,2,2,4}*224, {7,2,4,2}*224, {14,2,2,2}*224
   3-fold covers : {7,2,2,6}*336, {7,2,6,2}*336, {21,2,2,2}*336
   4-fold covers : {7,2,4,4}*448, {7,2,2,8}*448, {7,2,8,2}*448, {28,2,2,2}*448, {14,2,2,4}*448, {14,2,4,2}*448, {14,4,2,2}*448
   5-fold covers : {7,2,2,10}*560, {7,2,10,2}*560, {35,2,2,2}*560
   6-fold covers : {7,2,2,12}*672, {7,2,12,2}*672, {7,2,4,6}*672a, {7,2,6,4}*672a, {21,2,2,4}*672, {21,2,4,2}*672, {14,2,2,6}*672, {14,2,6,2}*672, {14,6,2,2}*672, {42,2,2,2}*672
   7-fold covers : {49,2,2,2}*784, {7,2,2,14}*784, {7,2,14,2}*784, {7,14,2,2}*784
   8-fold covers : {7,2,4,8}*896a, {7,2,8,4}*896a, {7,2,4,8}*896b, {7,2,8,4}*896b, {7,2,4,4}*896, {7,2,2,16}*896, {7,2,16,2}*896, {28,4,2,2}*896, {28,2,2,4}*896, {28,2,4,2}*896, {14,2,4,4}*896, {14,4,4,2}*896, {14,4,2,4}*896, {56,2,2,2}*896, {14,2,2,8}*896, {14,2,8,2}*896, {14,8,2,2}*896
   9-fold covers : {7,2,2,18}*1008, {7,2,18,2}*1008, {63,2,2,2}*1008, {7,2,6,6}*1008a, {7,2,6,6}*1008b, {7,2,6,6}*1008c, {21,2,2,6}*1008, {21,2,6,2}*1008, {21,6,2,2}*1008
   10-fold covers : {7,2,2,20}*1120, {7,2,20,2}*1120, {7,2,4,10}*1120, {7,2,10,4}*1120, {35,2,2,4}*1120, {35,2,4,2}*1120, {14,2,2,10}*1120, {14,2,10,2}*1120, {14,10,2,2}*1120, {70,2,2,2}*1120
   11-fold covers : {7,2,2,22}*1232, {7,2,22,2}*1232, {77,2,2,2}*1232
   12-fold covers : {7,2,4,12}*1344a, {7,2,12,4}*1344a, {7,2,2,24}*1344, {7,2,24,2}*1344, {7,2,6,8}*1344, {7,2,8,6}*1344, {21,2,4,4}*1344, {21,2,2,8}*1344, {21,2,8,2}*1344, {14,2,2,12}*1344, {14,2,12,2}*1344, {14,12,2,2}*1344, {28,2,2,6}*1344, {28,2,6,2}*1344, {28,6,2,2}*1344a, {14,2,4,6}*1344a, {14,2,6,4}*1344a, {14,4,2,6}*1344, {14,4,6,2}*1344, {14,6,2,4}*1344, {14,6,4,2}*1344a, {84,2,2,2}*1344, {42,2,2,4}*1344, {42,2,4,2}*1344, {42,4,2,2}*1344a, {7,2,4,6}*1344, {7,2,6,4}*1344, {7,2,6,6}*1344, {21,6,2,2}*1344, {21,4,2,2}*1344
   13-fold covers : {7,2,2,26}*1456, {7,2,26,2}*1456, {91,2,2,2}*1456
   14-fold covers : {49,2,2,4}*1568, {49,2,4,2}*1568, {98,2,2,2}*1568, {7,2,2,28}*1568, {7,2,28,2}*1568, {7,2,4,14}*1568, {7,2,14,4}*1568, {7,14,2,4}*1568, {7,14,4,2}*1568, {14,2,2,14}*1568, {14,2,14,2}*1568, {14,14,2,2}*1568a, {14,14,2,2}*1568c
   15-fold covers : {7,2,6,10}*1680, {7,2,10,6}*1680, {7,2,2,30}*1680, {7,2,30,2}*1680, {21,2,2,10}*1680, {21,2,10,2}*1680, {35,2,2,6}*1680, {35,2,6,2}*1680, {105,2,2,2}*1680
   16-fold covers : {7,2,4,8}*1792a, {7,2,8,4}*1792a, {7,2,8,8}*1792a, {7,2,8,8}*1792b, {7,2,8,8}*1792c, {7,2,8,8}*1792d, {7,2,4,16}*1792a, {7,2,16,4}*1792a, {7,2,4,16}*1792b, {7,2,16,4}*1792b, {7,2,4,4}*1792, {7,2,4,8}*1792b, {7,2,8,4}*1792b, {7,2,2,32}*1792, {7,2,32,2}*1792, {14,4,4,4}*1792, {28,4,4,2}*1792, {28,2,4,4}*1792, {28,4,2,4}*1792, {14,2,4,8}*1792a, {14,2,8,4}*1792a, {14,4,8,2}*1792a, {14,8,4,2}*1792a, {28,8,2,2}*1792a, {56,4,2,2}*1792a, {14,2,4,8}*1792b, {14,2,8,4}*1792b, {14,4,8,2}*1792b, {14,8,4,2}*1792b, {28,8,2,2}*1792b, {56,4,2,2}*1792b, {14,2,4,4}*1792, {14,4,4,2}*1792, {28,4,2,2}*1792, {14,4,2,8}*1792, {14,8,2,4}*1792, {28,2,2,8}*1792, {28,2,8,2}*1792, {56,2,2,4}*1792, {56,2,4,2}*1792, {14,2,2,16}*1792, {14,2,16,2}*1792, {14,16,2,2}*1792, {112,2,2,2}*1792
   17-fold covers : {7,2,2,34}*1904, {7,2,34,2}*1904, {119,2,2,2}*1904
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (8,9);;
s3 := (10,11);;
s4 := (12,13);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(2,3)(4,5)(6,7);
s1 := Sym(13)!(1,2)(3,4)(5,6);
s2 := Sym(13)!(8,9);
s3 := Sym(13)!(10,11);
s4 := Sym(13)!(12,13);
poly := sub<Sym(13)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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