Polytope of Type {15,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,24}*1440
if this polytope has a name.
Group : SmallGroup(1440,3578)
Rank : 4
Schlafli Type : {15,2,24}
Number of vertices, edges, etc : 15, 15, 24, 24
Order of s₀s₁s₂s₃ : 120
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 : {15,2,12}*720
   3-fold quotients : {5,2,24}*480, {15,2,8}*480
   4-fold quotients : {15,2,6}*360
   5-fold quotients : {3,2,24}*288
   6-fold quotients : {5,2,12}*240, {15,2,4}*240
   8-fold quotients : {15,2,3}*180
   9-fold quotients : {5,2,8}*160
   10-fold quotients : {3,2,12}*144
   12-fold quotients : {5,2,6}*120, {15,2,2}*120
   15-fold quotients : {3,2,8}*96
   18-fold quotients : {5,2,4}*80
   20-fold quotients : {3,2,6}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {3,2,4}*48
   36-fold quotients : {5,2,2}*40
   40-fold quotients : {3,2,3}*36
   60-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 := (17,18)(19,20)(21,24)(22,26)(23,25)(27,30)(28,32)(29,31)(34,37)(35,36)
(38,39);;
s3 := (16,22)(17,19)(18,28)(20,23)(21,25)(24,34)(26,29)(27,31)(30,38)(32,35)
(33,36)(37,39);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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