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Polytope of Type {12,10,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10,2,2}*960
if this polytope has a name.
Group : SmallGroup(960,11208)
Rank : 5
Schlafli Type : {12,10,2,2}
Number of vertices, edges, etc : 12, 60, 10, 2, 2
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,10,2,2,2} of size 1920
Vertex Figure Of :
   {2,12,10,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,10,2,2}*480
   3-fold quotients : {4,10,2,2}*320
   5-fold quotients : {12,2,2,2}*192
   6-fold quotients : {2,10,2,2}*160
   10-fold quotients : {6,2,2,2}*96
   12-fold quotients : {2,5,2,2}*80
   15-fold quotients : {4,2,2,2}*64
   20-fold quotients : {3,2,2,2}*48
   30-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,20,2,2}*1920, {12,10,2,4}*1920, {12,10,4,2}*1920, {24,10,2,2}*1920
Permutation Representation (GAP) :
s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)
(31,46)(32,47)(33,48)(34,49)(35,50)(36,56)(37,57)(38,58)(39,59)(40,60)(41,51)
(42,52)(43,53)(44,54)(45,55);;
s1 := ( 1,36)( 2,40)( 3,39)( 4,38)( 5,37)( 6,31)( 7,35)( 8,34)( 9,33)(10,32)
(11,41)(12,45)(13,44)(14,43)(15,42)(16,51)(17,55)(18,54)(19,53)(20,52)(21,46)
(22,50)(23,49)(24,48)(25,47)(26,56)(27,60)(28,59)(29,58)(30,57);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)
(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)(51,52)
(53,55)(56,57)(58,60);;
s3 := (61,62);;
s4 := (63,64);;
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, 
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(64)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)
(25,30)(31,46)(32,47)(33,48)(34,49)(35,50)(36,56)(37,57)(38,58)(39,59)(40,60)
(41,51)(42,52)(43,53)(44,54)(45,55);
s1 := Sym(64)!( 1,36)( 2,40)( 3,39)( 4,38)( 5,37)( 6,31)( 7,35)( 8,34)( 9,33)
(10,32)(11,41)(12,45)(13,44)(14,43)(15,42)(16,51)(17,55)(18,54)(19,53)(20,52)
(21,46)(22,50)(23,49)(24,48)(25,47)(26,56)(27,60)(28,59)(29,58)(30,57);
s2 := Sym(64)!( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)
(23,25)(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(41,42)(43,45)(46,47)(48,50)
(51,52)(53,55)(56,57)(58,60);
s3 := Sym(64)!(61,62);
s4 := Sym(64)!(63,64);
poly := sub<Sym(64)|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, 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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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