Polytope of Type {6,2,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,30}*1440
if this polytope has a name.
Group : SmallGroup(1440,5949)
Rank : 5
Schlafli Type : {6,2,2,30}
Number of vertices, edges, etc : 6, 6, 2, 30, 30
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {3,2,2,30}*720, {6,2,2,15}*720
   3-fold quotients : {6,2,2,10}*480, {2,2,2,30}*480
   4-fold quotients : {3,2,2,15}*360
   5-fold quotients : {6,2,2,6}*288
   6-fold quotients : {3,2,2,10}*240, {6,2,2,5}*240, {2,2,2,15}*240
   9-fold quotients : {2,2,2,10}*160
   10-fold quotients : {3,2,2,6}*144, {6,2,2,3}*144
   12-fold quotients : {3,2,2,5}*120
   15-fold quotients : {2,2,2,6}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,2,5}*80
   20-fold quotients : {3,2,2,3}*72
   30-fold quotients : {2,2,2,3}*48, {3,2,2,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

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