Polytope of Type {2,30,2,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,2,4,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,236171)
Rank : 6
Schlafli Type : {2,30,2,4,2}
Number of vertices, edges, etc : 2, 30, 30, 4, 4, 2
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,15,2,4,2}*960, {2,30,2,2,2}*960
   3-fold quotients : {2,10,2,4,2}*640
   4-fold quotients : {2,15,2,2,2}*480
   5-fold quotients : {2,6,2,4,2}*384
   6-fold quotients : {2,5,2,4,2}*320, {2,10,2,2,2}*320
   10-fold quotients : {2,3,2,4,2}*192, {2,6,2,2,2}*192
   12-fold quotients : {2,5,2,2,2}*160
   15-fold quotients : {2,2,2,4,2}*128
   20-fold quotients : {2,3,2,2,2}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,18)(19,22)(20,21)(23,24)
(25,28)(26,27)(29,32)(30,31);;
s2 := ( 3,19)( 4,13)( 5,11)( 6,21)( 7, 9)( 8,29)(10,15)(12,25)(14,23)(16,31)
(17,20)(18,30)(22,27)(24,26)(28,32);;
s3 := (34,35);;
s4 := (33,34)(35,36);;
s5 := (37,38);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
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*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(38)!(1,2);
s1 := Sym(38)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,16)(14,15)(17,18)(19,22)(20,21)
(23,24)(25,28)(26,27)(29,32)(30,31);
s2 := Sym(38)!( 3,19)( 4,13)( 5,11)( 6,21)( 7, 9)( 8,29)(10,15)(12,25)(14,23)
(16,31)(17,20)(18,30)(22,27)(24,26)(28,32);
s3 := Sym(38)!(34,35);
s4 := Sym(38)!(33,34)(35,36);
s5 := Sym(38)!(37,38);
poly := sub<Sym(38)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4, 
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*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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