Polytope of Type {10,6,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope