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Polytope of Type {52,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,4}*416
Also Known As : {52,4|2}. if this polytope has another name.
Group : SmallGroup(416,103)
Rank : 3
Schlafli Type : {52,4}
Number of vertices, edges, etc : 52, 104, 4
Order of s0s1s2 : 52
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {52,4,2} of size 832
   {52,4,4} of size 1664
Vertex Figure Of :
   {2,52,4} of size 832
   {4,52,4} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {52,2}*208, {26,4}*208
   4-fold quotients : {26,2}*104
   8-fold quotients : {13,2}*52
   13-fold quotients : {4,4}*32
   26-fold quotients : {2,4}*16, {4,2}*16
   52-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {104,4}*832a, {52,4}*832, {104,4}*832b, {52,8}*832a, {52,8}*832b
   3-fold covers : {52,12}*1248, {156,4}*1248a
   4-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
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)
( 53, 79)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 87)( 59, 86)( 60, 85)
( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 92)( 67,104)( 68,103)
( 69,102)( 70,101)( 71,100)( 72, 99)( 73, 98)( 74, 97)( 75, 96)( 76, 95)
( 77, 94)( 78, 93);;
s1 := (  1, 54)(  2, 53)(  3, 65)(  4, 64)(  5, 63)(  6, 62)(  7, 61)(  8, 60)
(  9, 59)( 10, 58)( 11, 57)( 12, 56)( 13, 55)( 14, 67)( 15, 66)( 16, 78)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 70)
( 25, 69)( 26, 68)( 27, 80)( 28, 79)( 29, 91)( 30, 90)( 31, 89)( 32, 88)
( 33, 87)( 34, 86)( 35, 85)( 36, 84)( 37, 83)( 38, 82)( 39, 81)( 40, 93)
( 41, 92)( 42,104)( 43,103)( 44,102)( 45,101)( 46,100)( 47, 99)( 48, 98)
( 49, 97)( 50, 96)( 51, 95)( 52, 94);;
s2 := ( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)
( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)( 81, 94)
( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)
( 90,103)( 91,104);;
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*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(104)!(  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)( 53, 79)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 87)( 59, 86)
( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 92)( 67,104)
( 68,103)( 69,102)( 70,101)( 71,100)( 72, 99)( 73, 98)( 74, 97)( 75, 96)
( 76, 95)( 77, 94)( 78, 93);
s1 := Sym(104)!(  1, 54)(  2, 53)(  3, 65)(  4, 64)(  5, 63)(  6, 62)(  7, 61)
(  8, 60)(  9, 59)( 10, 58)( 11, 57)( 12, 56)( 13, 55)( 14, 67)( 15, 66)
( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)
( 24, 70)( 25, 69)( 26, 68)( 27, 80)( 28, 79)( 29, 91)( 30, 90)( 31, 89)
( 32, 88)( 33, 87)( 34, 86)( 35, 85)( 36, 84)( 37, 83)( 38, 82)( 39, 81)
( 40, 93)( 41, 92)( 42,104)( 43,103)( 44,102)( 45,101)( 46,100)( 47, 99)
( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94);
s2 := Sym(104)!( 53, 66)( 54, 67)( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)
( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 79, 92)( 80, 93)
( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)
( 89,102)( 90,103)( 91,104);
poly := sub<Sym(104)|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*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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