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Polytope of Type {2,15,10}

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

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