Polytope of Type {5,2,12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150673)
Rank : 5
Schlafli Type : {5,2,12,8}
Number of vertices, edges, etc : 5, 5, 12, 48, 8
Order of s₀s₁s₂s₃s₄ : 120
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 : {5,2,12,4}*960a
   3-fold quotients : {5,2,4,8}*640b
   4-fold quotients : {5,2,12,2}*480, {5,2,6,4}*480a
   6-fold quotients : {5,2,4,4}*320
   8-fold quotients : {5,2,6,2}*240
   12-fold quotients : {5,2,2,4}*160, {5,2,4,2}*160
   16-fold quotients : {5,2,3,2}*120
   24-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)(10,11)(12,15)(13,17)(14,16)(19,20)(22,23)(24,27)(25,29)(26,28);;
s3 := ( 6, 7)( 9,10)(12,16)(13,15)(14,17)(18,25)(19,24)(20,26)(21,28)(22,27)
(23,29);;
s4 := ( 6,18)( 7,19)( 8,20)( 9,21)(10,22)(11,23)(12,27)(13,28)(14,29)(15,24)
(16,25)(17,26);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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