Polytope of Type {4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4}*1352
Also Known As : {4,4}_(13,0), {4,4|13}. if this polytope has another name.
Group : SmallGroup(1352,43)
Rank : 3
Schlafli Type : {4,4}
Number of vertices, edges, etc : 169, 338, 169
Order of s₀s₁s₂ : 26
Order of s₀s₁s₂s₁ : 13
Special Properties :
   Toroidal
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,157)(  3,144)(  4,131)(  5,118)(  6,105)(  7, 92)(  8, 79)(  9, 66)
( 10, 53)( 11, 40)( 12, 27)( 13, 14)( 15,169)( 16,156)( 17,143)( 18,130)
( 19,117)( 20,104)( 21, 91)( 22, 78)( 23, 65)( 24, 52)( 25, 39)( 28,168)
( 29,155)( 30,142)( 31,129)( 32,116)( 33,103)( 34, 90)( 35, 77)( 36, 64)
( 37, 51)( 41,167)( 42,154)( 43,141)( 44,128)( 45,115)( 46,102)( 47, 89)
( 48, 76)( 49, 63)( 54,166)( 55,153)( 56,140)( 57,127)( 58,114)( 59,101)
( 60, 88)( 61, 75)( 67,165)( 68,152)( 69,139)( 70,126)( 71,113)( 72,100)
( 73, 87)( 80,164)( 81,151)( 82,138)( 83,125)( 84,112)( 85, 99)( 93,163)
( 94,150)( 95,137)( 96,124)( 97,111)(106,162)(107,149)(108,136)(109,123)
(119,161)(120,148)(121,135)(132,160)(133,147)(145,159);;
s1 := (  2,105)(  3, 40)(  4,144)(  5, 79)(  6, 14)(  7,118)(  8, 53)(  9,157)
( 10, 92)( 11, 27)( 12,131)( 13, 66)( 15,110)( 16, 45)( 17,149)( 18, 84)
( 20,123)( 21, 58)( 22,162)( 23, 97)( 24, 32)( 25,136)( 26, 71)( 28,115)
( 29, 50)( 30,154)( 31, 89)( 33,128)( 34, 63)( 35,167)( 36,102)( 38,141)
( 39, 76)( 41,107)( 43,146)( 44, 81)( 46,120)( 47, 55)( 48,159)( 49, 94)
( 51,133)( 52, 68)( 54,112)( 56,151)( 57, 86)( 59,125)( 61,164)( 62, 99)
( 64,138)( 65, 73)( 67,117)( 69,156)( 70, 91)( 72,130)( 74,169)( 75,104)
( 77,143)( 80,109)( 82,148)( 85,122)( 87,161)( 88, 96)( 90,135)( 93,114)
( 95,153)( 98,127)(100,166)(103,140)(108,145)(111,119)(113,158)(116,132)
(121,150)(126,163)(129,137)(134,155)(139,168)(152,160);;
s2 := (  1,158)(  3, 15)(  4, 28)(  5, 41)(  6, 54)(  7, 67)(  8, 80)(  9, 93)
( 10,106)( 11,119)( 12,132)( 13,145)( 14,159)( 17, 29)( 18, 42)( 19, 55)
( 20, 68)( 21, 81)( 22, 94)( 23,107)( 24,120)( 25,133)( 26,146)( 27,160)
( 31, 43)( 32, 56)( 33, 69)( 34, 82)( 35, 95)( 36,108)( 37,121)( 38,134)
( 39,147)( 40,161)( 45, 57)( 46, 70)( 47, 83)( 48, 96)( 49,109)( 50,122)
( 51,135)( 52,148)( 53,162)( 59, 71)( 60, 84)( 61, 97)( 62,110)( 63,123)
( 64,136)( 65,149)( 66,163)( 73, 85)( 74, 98)( 75,111)( 76,124)( 77,137)
( 78,150)( 79,164)( 87, 99)( 88,112)( 89,125)( 90,138)( 91,151)( 92,165)
(101,113)(102,126)(103,139)(104,152)(105,166)(115,127)(116,140)(117,153)
(118,167)(129,141)(130,154)(131,168)(143,155)(144,169);;
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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(169)!(  2,157)(  3,144)(  4,131)(  5,118)(  6,105)(  7, 92)(  8, 79)
(  9, 66)( 10, 53)( 11, 40)( 12, 27)( 13, 14)( 15,169)( 16,156)( 17,143)
( 18,130)( 19,117)( 20,104)( 21, 91)( 22, 78)( 23, 65)( 24, 52)( 25, 39)
( 28,168)( 29,155)( 30,142)( 31,129)( 32,116)( 33,103)( 34, 90)( 35, 77)
( 36, 64)( 37, 51)( 41,167)( 42,154)( 43,141)( 44,128)( 45,115)( 46,102)
( 47, 89)( 48, 76)( 49, 63)( 54,166)( 55,153)( 56,140)( 57,127)( 58,114)
( 59,101)( 60, 88)( 61, 75)( 67,165)( 68,152)( 69,139)( 70,126)( 71,113)
( 72,100)( 73, 87)( 80,164)( 81,151)( 82,138)( 83,125)( 84,112)( 85, 99)
( 93,163)( 94,150)( 95,137)( 96,124)( 97,111)(106,162)(107,149)(108,136)
(109,123)(119,161)(120,148)(121,135)(132,160)(133,147)(145,159);
s1 := Sym(169)!(  2,105)(  3, 40)(  4,144)(  5, 79)(  6, 14)(  7,118)(  8, 53)
(  9,157)( 10, 92)( 11, 27)( 12,131)( 13, 66)( 15,110)( 16, 45)( 17,149)
( 18, 84)( 20,123)( 21, 58)( 22,162)( 23, 97)( 24, 32)( 25,136)( 26, 71)
( 28,115)( 29, 50)( 30,154)( 31, 89)( 33,128)( 34, 63)( 35,167)( 36,102)
( 38,141)( 39, 76)( 41,107)( 43,146)( 44, 81)( 46,120)( 47, 55)( 48,159)
( 49, 94)( 51,133)( 52, 68)( 54,112)( 56,151)( 57, 86)( 59,125)( 61,164)
( 62, 99)( 64,138)( 65, 73)( 67,117)( 69,156)( 70, 91)( 72,130)( 74,169)
( 75,104)( 77,143)( 80,109)( 82,148)( 85,122)( 87,161)( 88, 96)( 90,135)
( 93,114)( 95,153)( 98,127)(100,166)(103,140)(108,145)(111,119)(113,158)
(116,132)(121,150)(126,163)(129,137)(134,155)(139,168)(152,160);
s2 := Sym(169)!(  1,158)(  3, 15)(  4, 28)(  5, 41)(  6, 54)(  7, 67)(  8, 80)
(  9, 93)( 10,106)( 11,119)( 12,132)( 13,145)( 14,159)( 17, 29)( 18, 42)
( 19, 55)( 20, 68)( 21, 81)( 22, 94)( 23,107)( 24,120)( 25,133)( 26,146)
( 27,160)( 31, 43)( 32, 56)( 33, 69)( 34, 82)( 35, 95)( 36,108)( 37,121)
( 38,134)( 39,147)( 40,161)( 45, 57)( 46, 70)( 47, 83)( 48, 96)( 49,109)
( 50,122)( 51,135)( 52,148)( 53,162)( 59, 71)( 60, 84)( 61, 97)( 62,110)
( 63,123)( 64,136)( 65,149)( 66,163)( 73, 85)( 74, 98)( 75,111)( 76,124)
( 77,137)( 78,150)( 79,164)( 87, 99)( 88,112)( 89,125)( 90,138)( 91,151)
( 92,165)(101,113)(102,126)(103,139)(104,152)(105,166)(115,127)(116,140)
(117,153)(118,167)(129,141)(130,154)(131,168)(143,155)(144,169);
poly := sub<Sym(169)|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*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
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