Polytope of Type {10,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,36}*1440
if this polytope has a name.
Group : SmallGroup(1440,1583)
Rank : 4
Schlafli Type : {10,2,36}
Number of vertices, edges, etc : 10, 10, 36, 36
Order of s₀s₁s₂s₃ : 180
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 : {5,2,36}*720, {10,2,18}*720
   3-fold quotients : {10,2,12}*480
   4-fold quotients : {5,2,18}*360, {10,2,9}*360
   5-fold quotients : {2,2,36}*288
   6-fold quotients : {5,2,12}*240, {10,2,6}*240
   8-fold quotients : {5,2,9}*180
   9-fold quotients : {10,2,4}*160
   10-fold quotients : {2,2,18}*144
   12-fold quotients : {5,2,6}*120, {10,2,3}*120
   15-fold quotients : {2,2,12}*96
   18-fold quotients : {5,2,4}*80, {10,2,2}*80
   20-fold quotients : {2,2,9}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {2,2,6}*48
   36-fold quotients : {5,2,2}*40
   45-fold quotients : {2,2,4}*32
   60-fold quotients : {2,2,3}*24
   90-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 := (12,13)(14,15)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)(31,32)
(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)(45,46);;
s3 := (11,17)(12,14)(13,23)(15,25)(16,19)(18,21)(20,31)(22,33)(24,27)(26,29)
(28,39)(30,41)(32,35)(34,37)(36,45)(38,42)(40,43)(44,46);;
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(46)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(46)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(46)!(12,13)(14,15)(17,20)(18,19)(21,22)(23,24)(25,28)(26,27)(29,30)
(31,32)(33,36)(34,35)(37,38)(39,40)(41,44)(42,43)(45,46);
s3 := Sym(46)!(11,17)(12,14)(13,23)(15,25)(16,19)(18,21)(20,31)(22,33)(24,27)
(26,29)(28,39)(30,41)(32,35)(34,37)(36,45)(38,42)(40,43)(44,46);
poly := sub<Sym(46)|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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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