Polytope of Type {30,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,2,6}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 4
Schlafli Type : {30,2,6}
Number of vertices, edges, etc : 30, 30, 6, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,2,6,2} of size 1440
Vertex Figure Of :
   {2,30,2,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,2,6}*360, {30,2,3}*360
   3-fold quotients : {10,2,6}*240, {30,2,2}*240
   4-fold quotients : {15,2,3}*180
   5-fold quotients : {6,2,6}*144
   6-fold quotients : {5,2,6}*120, {10,2,3}*120, {15,2,2}*120
   9-fold quotients : {10,2,2}*80
   10-fold quotients : {3,2,6}*72, {6,2,3}*72
   12-fold quotients : {5,2,3}*60
   15-fold quotients : {2,2,6}*48, {6,2,2}*48
   18-fold quotients : {5,2,2}*40
   20-fold quotients : {3,2,3}*36
   30-fold quotients : {2,2,3}*24, {3,2,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,2,12}*1440, {60,2,6}*1440, {30,4,6}*1440
Permutation Representation (GAP) :

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

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