Polytope of Type {8,2,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,60}*1920
if this polytope has a name.
Group : SmallGroup(1920,182091)
Rank : 4
Schlafli Type : {8,2,60}
Number of vertices, edges, etc : 8, 8, 60, 60
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 : {4,2,60}*960, {8,2,30}*960
   3-fold quotients : {8,2,20}*640
   4-fold quotients : {8,2,15}*480, {2,2,60}*480, {4,2,30}*480
   5-fold quotients : {8,2,12}*384
   6-fold quotients : {4,2,20}*320, {8,2,10}*320
   8-fold quotients : {4,2,15}*240, {2,2,30}*240
   10-fold quotients : {4,2,12}*192, {8,2,6}*192
   12-fold quotients : {8,2,5}*160, {2,2,20}*160, {4,2,10}*160
   15-fold quotients : {8,2,4}*128
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {8,2,3}*96, {2,2,12}*96, {4,2,6}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,2,4}*64, {8,2,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
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 := (10,11)(12,13)(14,15)(17,22)(18,21)(19,24)(20,23)(25,28)(26,27)(29,30)
(31,32)(33,34)(35,44)(36,43)(37,42)(38,41)(39,46)(40,45)(47,50)(48,49)(51,54)
(52,53)(55,56)(57,64)(58,63)(59,62)(60,61)(65,68)(66,67);;
s3 := ( 9,35)(10,25)(11,51)(12,19)(13,37)(14,17)(15,57)(16,41)(18,27)(20,47)
(21,33)(22,53)(23,31)(24,65)(26,39)(28,59)(29,36)(30,58)(32,43)(34,61)(38,49)
(40,48)(42,55)(44,67)(45,52)(46,66)(50,60)(54,63)(56,62)(64,68);;
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*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(68)!(2,3)(4,5)(6,7);
s1 := Sym(68)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(68)!(10,11)(12,13)(14,15)(17,22)(18,21)(19,24)(20,23)(25,28)(26,27)
(29,30)(31,32)(33,34)(35,44)(36,43)(37,42)(38,41)(39,46)(40,45)(47,50)(48,49)
(51,54)(52,53)(55,56)(57,64)(58,63)(59,62)(60,61)(65,68)(66,67);
s3 := Sym(68)!( 9,35)(10,25)(11,51)(12,19)(13,37)(14,17)(15,57)(16,41)(18,27)
(20,47)(21,33)(22,53)(23,31)(24,65)(26,39)(28,59)(29,36)(30,58)(32,43)(34,61)
(38,49)(40,48)(42,55)(44,67)(45,52)(46,66)(50,60)(54,63)(56,62)(64,68);
poly := sub<Sym(68)|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*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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