Polytope of Type {6,3,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,10}*1800
if this polytope has a name.
Group : SmallGroup(1800,575)
Rank : 4
Schlafli Type : {6,3,10}
Number of vertices, edges, etc : 6, 45, 75, 50
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {2,3,10}*600
   25-fold quotients : {6,3,2}*72
   75-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (26,51)(27,52)(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);;
s1 := ( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,32)( 7,31)( 8,35)( 9,34)(10,33)
(11,38)(12,37)(13,36)(14,40)(15,39)(16,44)(17,43)(18,42)(19,41)(20,45)(21,50)
(22,49)(23,48)(24,47)(25,46)(52,55)(53,54)(56,57)(58,60)(61,63)(64,65)(66,69)
(67,68)(71,75)(72,74);;
s2 := ( 2, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)(18,23)
(26,51)(27,57)(28,63)(29,69)(30,75)(31,71)(32,52)(33,58)(34,64)(35,70)(36,66)
(37,72)(38,53)(39,59)(40,65)(41,61)(42,67)(43,73)(44,54)(45,60)(46,56)(47,62)
(48,68)(49,74)(50,55);;
s3 := ( 1,12)( 2,11)( 3,15)( 4,14)( 5,13)( 6, 7)( 8,10)(16,22)(17,21)(18,25)
(19,24)(20,23)(26,37)(27,36)(28,40)(29,39)(30,38)(31,32)(33,35)(41,47)(42,46)
(43,50)(44,49)(45,48)(51,62)(52,61)(53,65)(54,64)(55,63)(56,57)(58,60)(66,72)
(67,71)(68,75)(69,74)(70,73);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
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(75)!(26,51)(27,52)(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);
s1 := Sym(75)!( 1,26)( 2,30)( 3,29)( 4,28)( 5,27)( 6,32)( 7,31)( 8,35)( 9,34)
(10,33)(11,38)(12,37)(13,36)(14,40)(15,39)(16,44)(17,43)(18,42)(19,41)(20,45)
(21,50)(22,49)(23,48)(24,47)(25,46)(52,55)(53,54)(56,57)(58,60)(61,63)(64,65)
(66,69)(67,68)(71,75)(72,74);
s2 := Sym(75)!( 2, 7)( 3,13)( 4,19)( 5,25)( 6,21)( 9,14)(10,20)(11,16)(12,22)
(18,23)(26,51)(27,57)(28,63)(29,69)(30,75)(31,71)(32,52)(33,58)(34,64)(35,70)
(36,66)(37,72)(38,53)(39,59)(40,65)(41,61)(42,67)(43,73)(44,54)(45,60)(46,56)
(47,62)(48,68)(49,74)(50,55);
s3 := Sym(75)!( 1,12)( 2,11)( 3,15)( 4,14)( 5,13)( 6, 7)( 8,10)(16,22)(17,21)
(18,25)(19,24)(20,23)(26,37)(27,36)(28,40)(29,39)(30,38)(31,32)(33,35)(41,47)
(42,46)(43,50)(44,49)(45,48)(51,62)(52,61)(53,65)(54,64)(55,63)(56,57)(58,60)
(66,72)(67,71)(68,75)(69,74)(70,73);
poly := sub<Sym(75)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
to this polytope