Polytope of Type {2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,6}*1800
if this polytope has a name.
Group : SmallGroup(1800,586)
Rank : 4
Schlafli Type : {2,30,6}
Number of vertices, edges, etc : 2, 75, 225, 15
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,10,6}*600
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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 := ( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,37)( 9,36)(10,35)(11,34)(12,33)
(13,40)(14,39)(15,38)(16,42)(17,41)(18,43)(19,47)(20,46)(21,45)(22,44)(23,51)
(24,50)(25,49)(26,48)(27,52)(53,54)(55,57)(58,62)(59,61)(63,65)(66,67)(69,72)
(70,71)(73,76)(74,75);;
s3 := ( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)(20,23)
(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)(54,76)
(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
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)!( 3,29)( 4,28)( 5,32)( 6,31)( 7,30)( 8,37)( 9,36)(10,35)(11,34)
(12,33)(13,40)(14,39)(15,38)(16,42)(17,41)(18,43)(19,47)(20,46)(21,45)(22,44)
(23,51)(24,50)(25,49)(26,48)(27,52)(53,54)(55,57)(58,62)(59,61)(63,65)(66,67)
(69,72)(70,71)(73,76)(74,75);
s3 := Sym(77)!( 4,26)( 5,19)( 6,17)( 7,10)( 8,16)(11,25)(12,18)(13,24)(14,22)
(20,23)(29,51)(30,44)(31,42)(32,35)(33,41)(36,50)(37,43)(38,49)(39,47)(45,48)
(54,76)(55,69)(56,67)(57,60)(58,66)(61,75)(62,68)(63,74)(64,72)(70,73);
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*s3*s1*s2*s3*s1*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;

to this polytope