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Polytope of Type {12,2,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,28}*1344
if this polytope has a name.
Group : SmallGroup(1344,7252)
Rank : 4
Schlafli Type : {12,2,28}
Number of vertices, edges, etc : 12, 12, 28, 28
Order of s0s1s2s3 : 84
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,14}*672, {6,2,28}*672
   3-fold quotients : {4,2,28}*448
   4-fold quotients : {12,2,7}*336, {3,2,28}*336, {6,2,14}*336
   6-fold quotients : {2,2,28}*224, {4,2,14}*224
   7-fold quotients : {12,2,4}*192
   8-fold quotients : {3,2,14}*168, {6,2,7}*168
   12-fold quotients : {4,2,7}*112, {2,2,14}*112
   14-fold quotients : {12,2,2}*96, {6,2,4}*96
   16-fold quotients : {3,2,7}*84
   21-fold quotients : {4,2,4}*64
   24-fold quotients : {2,2,7}*56
   28-fold quotients : {3,2,4}*48, {6,2,2}*48
   42-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {3,2,2}*24
   84-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,15)(16,17)(19,22)(20,21)(23,24)(25,26)(27,30)(28,29)(31,32)(33,34)
(35,38)(36,37)(39,40);;
s3 := (13,19)(14,16)(15,25)(17,27)(18,21)(20,23)(22,33)(24,35)(26,29)(28,31)
(30,39)(32,36)(34,37)(38,40);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(40)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(40)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(40)!(14,15)(16,17)(19,22)(20,21)(23,24)(25,26)(27,30)(28,29)(31,32)
(33,34)(35,38)(36,37)(39,40);
s3 := Sym(40)!(13,19)(14,16)(15,25)(17,27)(18,21)(20,23)(22,33)(24,35)(26,29)
(28,31)(30,39)(32,36)(34,37)(38,40);
poly := sub<Sym(40)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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