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Polytope of Type {26,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,4}*208
Also Known As : {26,4|2}. if this polytope has another name.
Group : SmallGroup(208,39)
Rank : 3
Schlafli Type : {26,4}
Number of vertices, edges, etc : 26, 52, 4
Order of s0s1s2 : 52
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {26,4,2} of size 416
   {26,4,4} of size 832
   {26,4,6} of size 1248
   {26,4,3} of size 1248
   {26,4,8} of size 1664
   {26,4,8} of size 1664
   {26,4,4} of size 1664
   {26,4,6} of size 1872
Vertex Figure Of :
   {2,26,4} of size 416
   {4,26,4} of size 832
   {6,26,4} of size 1248
   {8,26,4} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {26,2}*104
   4-fold quotients : {13,2}*52
   13-fold quotients : {2,4}*16
   26-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {52,4}*416, {26,8}*416
   3-fold covers : {26,12}*624, {78,4}*624a
   4-fold covers : {104,4}*832a, {52,4}*832, {104,4}*832b, {52,8}*832a, {52,8}*832b, {26,16}*832
   5-fold covers : {26,20}*1040, {130,4}*1040
   6-fold covers : {26,24}*1248, {52,12}*1248, {156,4}*1248a, {78,8}*1248
   7-fold covers : {26,28}*1456, {182,4}*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, {26,32}*1664
   9-fold covers : {26,36}*1872, {234,4}*1872a, {78,12}*1872a, {78,12}*1872b, {78,12}*1872c, {78,4}*1872
Permutation Representation (GAP) :
s0 := ( 2,13)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(15,26)(16,25)(17,24)(18,23)
(19,22)(20,21)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(41,52)(42,51)(43,50)
(44,49)(45,48)(46,47);;
s1 := ( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)(18,24)
(19,23)(20,22)(27,41)(28,40)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)
(36,45)(37,44)(38,43)(39,42);;
s2 := ( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)(10,36)
(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)(21,47)
(22,48)(23,49)(24,50)(25,51)(26,52);;
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(52)!( 2,13)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(15,26)(16,25)(17,24)
(18,23)(19,22)(20,21)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(41,52)(42,51)
(43,50)(44,49)(45,48)(46,47);
s1 := Sym(52)!( 1, 2)( 3,13)( 4,12)( 5,11)( 6,10)( 7, 9)(14,15)(16,26)(17,25)
(18,24)(19,23)(20,22)(27,41)(28,40)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)
(35,46)(36,45)(37,44)(38,43)(39,42);
s2 := Sym(52)!( 1,27)( 2,28)( 3,29)( 4,30)( 5,31)( 6,32)( 7,33)( 8,34)( 9,35)
(10,36)(11,37)(12,38)(13,39)(14,40)(15,41)(16,42)(17,43)(18,44)(19,45)(20,46)
(21,47)(22,48)(23,49)(24,50)(25,51)(26,52);
poly := sub<Sym(52)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 >; 
 
References : None.
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