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

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

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