Polytope of Type {15,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,30}*1800
if this polytope has a name.
Group : SmallGroup(1800,736)
Rank : 4
Schlafli Type : {15,2,30}
Number of vertices, edges, etc : 15, 15, 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 : {15,2,15}*900
   3-fold quotients : {5,2,30}*600, {15,2,10}*600
   5-fold quotients : {3,2,30}*360, {15,2,6}*360
   6-fold quotients : {5,2,15}*300, {15,2,5}*300
   9-fold quotients : {5,2,10}*200
   10-fold quotients : {3,2,15}*180, {15,2,3}*180
   15-fold quotients : {3,2,10}*120, {5,2,6}*120, {15,2,2}*120
   18-fold quotients : {5,2,5}*100
   25-fold quotients : {3,2,6}*72
   30-fold quotients : {3,2,5}*60, {5,2,3}*60
   45-fold quotients : {5,2,2}*40
   50-fold quotients : {3,2,3}*36
   75-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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