Polytope of Type {52,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,2}*208
if this polytope has a name.
Group : SmallGroup(208,37)
Rank : 3
Schlafli Type : {52,2}
Number of vertices, edges, etc : 52, 52, 2
Order of s₀s₁s₂ : 52
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {52,2,2} of size 416
   {52,2,3} of size 624
   {52,2,4} of size 832
   {52,2,5} of size 1040
   {52,2,6} of size 1248
   {52,2,7} of size 1456
   {52,2,8} of size 1664
   {52,2,9} of size 1872
Vertex Figure Of :
   {2,52,2} of size 416
   {4,52,2} of size 832
   {6,52,2} of size 1248
   {6,52,2} of size 1248
   {8,52,2} of size 1664
   {8,52,2} of size 1664
   {4,52,2} of size 1664
   {6,52,2} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {26,2}*104
   4-fold quotients : {13,2}*52
   13-fold quotients : {4,2}*16
   26-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {52,4}*416, {104,2}*416
   3-fold covers : {52,6}*624a, {156,2}*624
   4-fold covers : {104,4}*832a, {52,4}*832, {104,4}*832b, {52,8}*832a, {52,8}*832b, {208,2}*832
   5-fold covers : {52,10}*1040, {260,2}*1040
   6-fold covers : {104,6}*1248, {52,12}*1248, {156,4}*1248a, {312,2}*1248
   7-fold covers : {52,14}*1456, {364,2}*1456
   8-fold covers : {52,8}*1664a, {104,4}*1664a, {104,8}*1664a, {104,8}*1664b, {104,8}*1664c, {104,8}*1664d, {52,16}*1664a, {208,4}*1664a, {52,16}*1664b, {208,4}*1664b, {52,4}*1664, {104,4}*1664b, {52,8}*1664b, {416,2}*1664
   9-fold covers : {52,18}*1872a, {468,2}*1872, {156,6}*1872a, {156,6}*1872b, {156,6}*1872c, {52,6}*1872
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(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);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(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)(42,51)(44,48)(46,49)(50,52);;
s2 := (53,54);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(54)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(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);
s1 := Sym(54)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(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)(42,51)(44,48)(46,49)(50,52);
s2 := Sym(54)!(53,54);
poly := sub<Sym(54)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

to this polytope