Polytope of Type {4,12,2,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12,2,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,205032)
Rank : 5
Schlafli Type : {4,12,2,10}
Number of vertices, edges, etc : 4, 24, 12, 10, 10
Order of s₀s₁s₂s₃s₄ : 60
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 : {4,12,2,5}*960a, {2,12,2,10}*960, {4,6,2,10}*960a
   3-fold quotients : {4,4,2,10}*640
   4-fold quotients : {2,12,2,5}*480, {4,6,2,5}*480a, {2,6,2,10}*480
   5-fold quotients : {4,12,2,2}*384a
   6-fold quotients : {4,4,2,5}*320, {2,4,2,10}*320, {4,2,2,10}*320
   8-fold quotients : {2,3,2,10}*240, {2,6,2,5}*240
   10-fold quotients : {2,12,2,2}*192, {4,6,2,2}*192a
   12-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160, {2,2,2,10}*160
   15-fold quotients : {4,4,2,2}*128
   16-fold quotients : {2,3,2,5}*120
   20-fold quotients : {2,6,2,2}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,3,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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