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Polytope of Type {2,6,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10,5}*1200
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 5
Schlafli Type : {2,6,10,5}
Number of vertices, edges, etc : 2, 6, 30, 25, 5
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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) :
   3-fold quotients : {2,2,10,5}*400
   5-fold quotients : {2,6,2,5}*240
   10-fold quotients : {2,3,2,5}*120
   15-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)(37,62)
(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)(48,73)
(49,74)(50,75)(51,76)(52,77);;
s2 := ( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,33)( 9,37)(10,36)(11,35)(12,34)
(13,38)(14,42)(15,41)(16,40)(17,39)(18,43)(19,47)(20,46)(21,45)(22,44)(23,48)
(24,52)(25,51)(26,50)(27,49)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)
(70,71)(74,77)(75,76);;
s3 := ( 3, 4)( 5, 7)( 8,24)( 9,23)(10,27)(11,26)(12,25)(13,19)(14,18)(15,22)
(16,21)(17,20)(28,29)(30,32)(33,49)(34,48)(35,52)(36,51)(37,50)(38,44)(39,43)
(40,47)(41,46)(42,45)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)(63,69)
(64,68)(65,72)(66,71)(67,70);;
s4 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)(17,24)
(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)(41,50)
(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)(65,76)
(66,75)(67,74)(69,72)(70,71);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(77)!(1,2);
s1 := Sym(77)!(28,53)(29,54)(30,55)(31,56)(32,57)(33,58)(34,59)(35,60)(36,61)
(37,62)(38,63)(39,64)(40,65)(41,66)(42,67)(43,68)(44,69)(45,70)(46,71)(47,72)
(48,73)(49,74)(50,75)(51,76)(52,77);
s2 := Sym(77)!( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,33)( 9,37)(10,36)(11,35)
(12,34)(13,38)(14,42)(15,41)(16,40)(17,39)(18,43)(19,47)(20,46)(21,45)(22,44)
(23,48)(24,52)(25,51)(26,50)(27,49)(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)
(69,72)(70,71)(74,77)(75,76);
s3 := Sym(77)!( 3, 4)( 5, 7)( 8,24)( 9,23)(10,27)(11,26)(12,25)(13,19)(14,18)
(15,22)(16,21)(17,20)(28,29)(30,32)(33,49)(34,48)(35,52)(36,51)(37,50)(38,44)
(39,43)(40,47)(41,46)(42,45)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)
(63,69)(64,68)(65,72)(66,71)(67,70);
s4 := Sym(77)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)
(17,24)(19,22)(20,21)(28,33)(29,37)(30,36)(31,35)(32,34)(38,48)(39,52)(40,51)
(41,50)(42,49)(44,47)(45,46)(53,58)(54,62)(55,61)(56,60)(57,59)(63,73)(64,77)
(65,76)(66,75)(67,74)(69,72)(70,71);
poly := sub<Sym(77)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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