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Polytope of Type {2,10,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,30}*1200a
if this polytope has a name.
Group : SmallGroup(1200,1006)
Rank : 4
Schlafli Type : {2,10,30}
Number of vertices, edges, etc : 2, 10, 150, 30
Order of s0s1s2s3 : 30
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) :
   3-fold quotients : {2,10,10}*400c
   5-fold quotients : {2,10,6}*240
   6-fold quotients : {2,5,10}*200
   15-fold quotients : {2,10,2}*80
   25-fold quotients : {2,2,6}*48
   30-fold quotients : {2,5,2}*40
   50-fold quotients : {2,2,3}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)(15,21)
(16,20)(17,19)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,43)(39,47)
(40,46)(41,45)(42,44)(54,57)(55,56)(58,73)(59,77)(60,76)(61,75)(62,74)(63,68)
(64,72)(65,71)(66,70)(67,69);;
s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,24)(14,23)(15,27)(16,26)(17,25)
(18,19)(20,22)(28,59)(29,58)(30,62)(31,61)(32,60)(33,54)(34,53)(35,57)(36,56)
(37,55)(38,74)(39,73)(40,77)(41,76)(42,75)(43,69)(44,68)(45,72)(46,71)(47,70)
(48,64)(49,63)(50,67)(51,66)(52,65);;
s3 := ( 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);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*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(77)!(1,2);
s1 := Sym(77)!( 4, 7)( 5, 6)( 8,23)( 9,27)(10,26)(11,25)(12,24)(13,18)(14,22)
(15,21)(16,20)(17,19)(29,32)(30,31)(33,48)(34,52)(35,51)(36,50)(37,49)(38,43)
(39,47)(40,46)(41,45)(42,44)(54,57)(55,56)(58,73)(59,77)(60,76)(61,75)(62,74)
(63,68)(64,72)(65,71)(66,70)(67,69);
s2 := Sym(77)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,24)(14,23)(15,27)(16,26)
(17,25)(18,19)(20,22)(28,59)(29,58)(30,62)(31,61)(32,60)(33,54)(34,53)(35,57)
(36,56)(37,55)(38,74)(39,73)(40,77)(41,76)(42,75)(43,69)(44,68)(45,72)(46,71)
(47,70)(48,64)(49,63)(50,67)(51,66)(52,65);
s3 := 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);
poly := sub<Sym(77)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s3*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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