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Polytope of Type {2,6,15}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,15}*360
if this polytope has a name.
Group : SmallGroup(360,154)
Rank : 4
Schlafli Type : {2,6,15}
Number of vertices, edges, etc : 2, 6, 45, 15
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,15,2} of size 720
   {2,6,15,4} of size 1440
Vertex Figure Of :
   {2,2,6,15} of size 720
   {3,2,6,15} of size 1080
   {4,2,6,15} of size 1440
   {5,2,6,15} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,15}*120
   5-fold quotients : {2,6,3}*72
   9-fold quotients : {2,2,5}*40
   15-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,15}*720, {2,6,30}*720c
   3-fold covers : {2,6,45}*1080, {2,6,15}*1080, {6,6,15}*1080b
   4-fold covers : {8,6,15}*1440, {2,6,60}*1440c, {4,6,30}*1440c, {2,12,30}*1440c, {2,12,15}*1440, {2,6,15}*1440e
   5-fold covers : {2,6,75}*1800, {10,6,15}*1800, {2,30,15}*1800
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)
(28,43)(29,44)(30,45)(31,46)(32,47);;
s2 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)
(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44);;
s3 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)
(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)
(32,45);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(47)!(1,2);
s1 := Sym(47)!(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)
(27,42)(28,43)(29,44)(30,45)(31,46)(32,47);
s2 := Sym(47)!( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)
(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)
(41,45)(42,44);
s3 := Sym(47)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)
(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)
(31,46)(32,45);
poly := sub<Sym(47)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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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