Polytope of Type {10,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,30}*1200
if this polytope has a name.
Group : SmallGroup(1200,1028)
Rank : 4
Schlafli Type : {10,2,30}
Number of vertices, edges, etc : 10, 10, 30, 30
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 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 : {5,2,30}*600, {10,2,15}*600
   3-fold quotients : {10,2,10}*400
   4-fold quotients : {5,2,15}*300
   5-fold quotients : {10,2,6}*240, {2,2,30}*240
   6-fold quotients : {5,2,10}*200, {10,2,5}*200
   10-fold quotients : {5,2,6}*120, {10,2,3}*120, {2,2,15}*120
   12-fold quotients : {5,2,5}*100
   15-fold quotients : {2,2,10}*80, {10,2,2}*80
   20-fold quotients : {5,2,3}*60
   25-fold quotients : {2,2,6}*48
   30-fold quotients : {2,2,5}*40, {5,2,2}*40
   50-fold quotients : {2,2,3}*24
   75-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (13,14)(15,16)(17,18)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)(31,32)
(33,36)(34,35)(37,40)(38,39);;
s3 := (11,27)(12,21)(13,19)(14,29)(15,17)(16,37)(18,23)(20,33)(22,31)(24,39)
(25,28)(26,38)(30,35)(32,34)(36,40);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(40)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(40)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(40)!(13,14)(15,16)(17,18)(19,20)(21,24)(22,23)(25,26)(27,30)(28,29)
(31,32)(33,36)(34,35)(37,40)(38,39);
s3 := Sym(40)!(11,27)(12,21)(13,19)(14,29)(15,17)(16,37)(18,23)(20,33)(22,31)
(24,39)(25,28)(26,38)(30,35)(32,34)(36,40);
poly := sub<Sym(40)|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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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*s2*s3*s2*s3 >;

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