Polytope of Type {8,2,52}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,52}*1664
if this polytope has a name.
Group : SmallGroup(1664,16186)
Rank : 4
Schlafli Type : {8,2,52}
Number of vertices, edges, etc : 8, 8, 52, 52
Order of s₀s₁s₂s₃ : 104
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 : {4,2,52}*832, {8,2,26}*832
   4-fold quotients : {8,2,13}*416, {2,2,52}*416, {4,2,26}*416
   8-fold quotients : {4,2,13}*208, {2,2,26}*208
   13-fold quotients : {8,2,4}*128
   16-fold quotients : {2,2,13}*104
   26-fold quotients : {4,2,4}*64, {8,2,2}*64
   52-fold quotients : {2,2,4}*32, {4,2,2}*32
   104-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)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)
(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44)(45,46)(47,50)(48,49)(51,52)
(53,54)(55,58)(56,57)(59,60);;
s3 := ( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)
(26,37)(28,39)(30,33)(32,35)(34,45)(36,47)(38,41)(40,43)(42,53)(44,55)(46,49)
(48,51)(50,59)(52,56)(54,57)(58,60);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(60)!(2,3)(4,5)(6,7);
s1 := Sym(60)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(60)!(10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)
(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44)(45,46)(47,50)(48,49)
(51,52)(53,54)(55,58)(56,57)(59,60);
s3 := Sym(60)!( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)
(24,27)(26,37)(28,39)(30,33)(32,35)(34,45)(36,47)(38,41)(40,43)(42,53)(44,55)
(46,49)(48,51)(50,59)(52,56)(54,57)(58,60);
poly := sub<Sym(60)|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 >;

to this polytope