Polytope of Type {8,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,30}*960
if this polytope has a name.
Group : SmallGroup(960,10708)
Rank : 4
Schlafli Type : {8,2,30}
Number of vertices, edges, etc : 8, 8, 30, 30
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,30,2} of size 1920
Vertex Figure Of :
   {2,8,2,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,2,15}*480, {4,2,30}*480
   3-fold quotients : {8,2,10}*320
   4-fold quotients : {4,2,15}*240, {2,2,30}*240
   5-fold quotients : {8,2,6}*192
   6-fold quotients : {8,2,5}*160, {4,2,10}*160
   8-fold quotients : {2,2,15}*120
   10-fold quotients : {8,2,3}*96, {4,2,6}*96
   12-fold quotients : {4,2,5}*80, {2,2,10}*80
   15-fold quotients : {8,2,2}*64
   20-fold quotients : {4,2,3}*48, {2,2,6}*48
   24-fold quotients : {2,2,5}*40
   30-fold quotients : {4,2,2}*32
   40-fold quotients : {2,2,3}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,30}*1920a, {8,2,60}*1920, {16,2,30}*1920
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);;
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, 
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(38)!(2,3)(4,5)(6,7);
s1 := Sym(38)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(38)!(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(38)!( 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);
poly := sub<Sym(38)|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, 
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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