Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*1800
if this polytope has a name.
Group : SmallGroup(1800,586)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 75, 225, 150
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 : {2,3,6}*600
   25-fold quotients : {2,3,6}*72
   75-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)(18,24)
(28,53)(29,60)(30,67)(31,69)(32,76)(33,70)(34,77)(35,54)(36,61)(37,63)(38,62)
(39,64)(40,71)(41,73)(42,55)(43,74)(44,56)(45,58)(46,65)(47,72)(48,66)(49,68)
(50,75)(51,57)(52,59);;
s2 := ( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,36)( 9,35)(10,34)(11,33)(12,37)
(13,39)(14,38)(15,42)(16,41)(17,40)(18,47)(19,46)(20,45)(21,44)(22,43)(23,50)
(24,49)(25,48)(26,52)(27,51)(54,57)(55,56)(58,61)(59,60)(63,64)(65,67)(68,72)
(69,71)(73,75)(76,77);;
s3 := ( 3,14)( 4,12)( 6,23)( 7,21)( 8,27)( 9,20)(10,13)(15,26)(16,19)(22,25)
(28,39)(29,37)(31,48)(32,46)(33,52)(34,45)(35,38)(40,51)(41,44)(47,50)(53,64)
(54,62)(56,73)(57,71)(58,77)(59,70)(60,63)(65,76)(66,69)(72,75);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(77)!(1,2);
s1 := Sym(77)!( 4,10)( 5,17)( 6,19)( 7,26)( 8,20)( 9,27)(12,13)(15,21)(16,23)
(18,24)(28,53)(29,60)(30,67)(31,69)(32,76)(33,70)(34,77)(35,54)(36,61)(37,63)
(38,62)(39,64)(40,71)(41,73)(42,55)(43,74)(44,56)(45,58)(46,65)(47,72)(48,66)
(49,68)(50,75)(51,57)(52,59);
s2 := Sym(77)!( 3,28)( 4,32)( 5,31)( 6,30)( 7,29)( 8,36)( 9,35)(10,34)(11,33)
(12,37)(13,39)(14,38)(15,42)(16,41)(17,40)(18,47)(19,46)(20,45)(21,44)(22,43)
(23,50)(24,49)(25,48)(26,52)(27,51)(54,57)(55,56)(58,61)(59,60)(63,64)(65,67)
(68,72)(69,71)(73,75)(76,77);
s3 := Sym(77)!( 3,14)( 4,12)( 6,23)( 7,21)( 8,27)( 9,20)(10,13)(15,26)(16,19)
(22,25)(28,39)(29,37)(31,48)(32,46)(33,52)(34,45)(35,38)(40,51)(41,44)(47,50)
(53,64)(54,62)(56,73)(57,71)(58,77)(59,70)(60,63)(65,76)(66,69)(72,75);
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, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;

to this polytope