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Polytope of Type {2,10,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,15}*600
if this polytope has a name.
Group : SmallGroup(600,195)
Rank : 4
Schlafli Type : {2,10,15}
Number of vertices, edges, etc : 2, 10, 75, 15
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,10,15,2} of size 1200
Vertex Figure Of :
   {2,2,10,15} of size 1200
   {3,2,10,15} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,5}*200
   5-fold quotients : {2,2,15}*120
   15-fold quotients : {2,2,5}*40
   25-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,10,15}*1200, {2,10,30}*1200c
   3-fold covers : {2,10,45}*1800, {6,10,15}*1800, {2,30,15}*1800
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)(17,22)
(33,48)(34,49)(35,50)(36,51)(37,52)(38,43)(39,44)(40,45)(41,46)(42,47)(58,73)
(59,74)(60,75)(61,76)(62,77)(63,68)(64,69)(65,70)(66,71)(67,72);;
s2 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(13,23)(14,27)(15,26)(16,25)(17,24)
(19,22)(20,21)(28,58)(29,62)(30,61)(31,60)(32,59)(33,53)(34,57)(35,56)(36,55)
(37,54)(38,73)(39,77)(40,76)(41,75)(42,74)(43,68)(44,72)(45,71)(46,70)(47,69)
(48,63)(49,67)(50,66)(51,65)(52,64);;
s3 := ( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)(12,50)
(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)(23,34)
(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)(62,75)
(63,69)(64,68)(65,72)(66,71)(67,70);;
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*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(77)!(1,2);
s1 := Sym(77)!( 8,23)( 9,24)(10,25)(11,26)(12,27)(13,18)(14,19)(15,20)(16,21)
(17,22)(33,48)(34,49)(35,50)(36,51)(37,52)(38,43)(39,44)(40,45)(41,46)(42,47)
(58,73)(59,74)(60,75)(61,76)(62,77)(63,68)(64,69)(65,70)(66,71)(67,72);
s2 := 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)(28,58)(29,62)(30,61)(31,60)(32,59)(33,53)(34,57)(35,56)
(36,55)(37,54)(38,73)(39,77)(40,76)(41,75)(42,74)(43,68)(44,72)(45,71)(46,70)
(47,69)(48,63)(49,67)(50,66)(51,65)(52,64);
s3 := Sym(77)!( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,49)( 9,48)(10,52)(11,51)
(12,50)(13,44)(14,43)(15,47)(16,46)(17,45)(18,39)(19,38)(20,42)(21,41)(22,40)
(23,34)(24,33)(25,37)(26,36)(27,35)(53,54)(55,57)(58,74)(59,73)(60,77)(61,76)
(62,75)(63,69)(64,68)(65,72)(66,71)(67,70);
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*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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