Polytope of Type {8,2,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,30,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235336)
Rank : 5
Schlafli Type : {8,2,30,2}
Number of vertices, edges, etc : 8, 8, 30, 30, 2
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {8,2,15,2}*960, {4,2,30,2}*960
   3-fold quotients : {8,2,10,2}*640
   4-fold quotients : {4,2,15,2}*480, {2,2,30,2}*480
   5-fold quotients : {8,2,6,2}*384
   6-fold quotients : {8,2,5,2}*320, {4,2,10,2}*320
   8-fold quotients : {2,2,15,2}*240
   10-fold quotients : {8,2,3,2}*192, {4,2,6,2}*192
   12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   15-fold quotients : {8,2,2,2}*128
   20-fold quotients : {4,2,3,2}*96, {2,2,6,2}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {4,2,2,2}*64
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)(29,30)
(31,34)(32,33)(35,38)(36,37);;
s3 := ( 9,25)(10,19)(11,17)(12,27)(13,15)(14,35)(16,21)(18,31)(20,29)(22,37)
(23,26)(24,36)(28,33)(30,32)(34,38);;
s4 := (39,40);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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)!(2,3)(4,5)(6,7);
s1 := Sym(40)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(40)!(11,12)(13,14)(15,16)(17,18)(19,22)(20,21)(23,24)(25,28)(26,27)
(29,30)(31,34)(32,33)(35,38)(36,37);
s3 := Sym(40)!( 9,25)(10,19)(11,17)(12,27)(13,15)(14,35)(16,21)(18,31)(20,29)
(22,37)(23,26)(24,36)(28,33)(30,32)(34,38);
s4 := Sym(40)!(39,40);
poly := sub<Sym(40)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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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