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Polytope of Type {2,26,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,6,3}*1872
if this polytope has a name.
Group : SmallGroup(1872,1061)
Rank : 5
Schlafli Type : {2,26,6,3}
Number of vertices, edges, etc : 2, 26, 78, 9, 3
Order of s0s1s2s3s4 : 78
Order of s0s1s2s3s4s3s2s1 : 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) :
   3-fold quotients : {2,26,2,3}*624
   6-fold quotients : {2,13,2,3}*312
   13-fold quotients : {2,2,6,3}*144
   39-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)
( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)( 85, 90)
( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)(100,101)
(108,119)(109,118)(110,117)(111,116)(112,115)(113,114);;
s2 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 30)( 17, 29)
( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)
( 26, 33)( 27, 32)( 28, 31)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)
( 48, 50)( 55, 69)( 56, 68)( 57, 80)( 58, 79)( 59, 78)( 60, 77)( 61, 76)
( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 71)( 67, 70)( 81, 82)( 83, 93)
( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 94,108)( 95,107)( 96,119)( 97,118)
( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)
(106,109);;
s3 := (  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)(  9, 22)( 10, 23)
( 11, 24)( 12, 25)( 13, 26)( 14, 27)( 15, 28)( 42, 94)( 43, 95)( 44, 96)
( 45, 97)( 46, 98)( 47, 99)( 48,100)( 49,101)( 50,102)( 51,103)( 52,104)
( 53,105)( 54,106)( 55, 81)( 56, 82)( 57, 83)( 58, 84)( 59, 85)( 60, 86)
( 61, 87)( 62, 88)( 63, 89)( 64, 90)( 65, 91)( 66, 92)( 67, 93)( 68,107)
( 69,108)( 70,109)( 71,110)( 72,111)( 73,112)( 74,113)( 75,114)( 76,115)
( 77,116)( 78,117)( 79,118)( 80,119);;
s4 := (  3, 42)(  4, 43)(  5, 44)(  6, 45)(  7, 46)(  8, 47)(  9, 48)( 10, 49)
( 11, 50)( 12, 51)( 13, 52)( 14, 53)( 15, 54)( 16, 68)( 17, 69)( 18, 70)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)( 26, 78)
( 27, 79)( 28, 80)( 29, 55)( 30, 56)( 31, 57)( 32, 58)( 33, 59)( 34, 60)
( 35, 61)( 36, 62)( 37, 63)( 38, 64)( 39, 65)( 40, 66)( 41, 67)( 94,107)
( 95,108)( 96,109)( 97,110)( 98,111)( 99,112)(100,113)(101,114)(102,115)
(103,116)(104,117)(105,118)(106,119);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(119)!(1,2);
s1 := Sym(119)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)
( 85, 90)( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)
(100,101)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114);
s2 := Sym(119)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 30)
( 17, 29)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)
( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 42, 43)( 44, 54)( 45, 53)( 46, 52)
( 47, 51)( 48, 50)( 55, 69)( 56, 68)( 57, 80)( 58, 79)( 59, 78)( 60, 77)
( 61, 76)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 71)( 67, 70)( 81, 82)
( 83, 93)( 84, 92)( 85, 91)( 86, 90)( 87, 89)( 94,108)( 95,107)( 96,119)
( 97,118)( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)
(105,110)(106,109);
s3 := Sym(119)!(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)(  9, 22)
( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 14, 27)( 15, 28)( 42, 94)( 43, 95)
( 44, 96)( 45, 97)( 46, 98)( 47, 99)( 48,100)( 49,101)( 50,102)( 51,103)
( 52,104)( 53,105)( 54,106)( 55, 81)( 56, 82)( 57, 83)( 58, 84)( 59, 85)
( 60, 86)( 61, 87)( 62, 88)( 63, 89)( 64, 90)( 65, 91)( 66, 92)( 67, 93)
( 68,107)( 69,108)( 70,109)( 71,110)( 72,111)( 73,112)( 74,113)( 75,114)
( 76,115)( 77,116)( 78,117)( 79,118)( 80,119);
s4 := Sym(119)!(  3, 42)(  4, 43)(  5, 44)(  6, 45)(  7, 46)(  8, 47)(  9, 48)
( 10, 49)( 11, 50)( 12, 51)( 13, 52)( 14, 53)( 15, 54)( 16, 68)( 17, 69)
( 18, 70)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)
( 26, 78)( 27, 79)( 28, 80)( 29, 55)( 30, 56)( 31, 57)( 32, 58)( 33, 59)
( 34, 60)( 35, 61)( 36, 62)( 37, 63)( 38, 64)( 39, 65)( 40, 66)( 41, 67)
( 94,107)( 95,108)( 96,109)( 97,110)( 98,111)( 99,112)(100,113)(101,114)
(102,115)(103,116)(104,117)(105,118)(106,119);
poly := sub<Sym(119)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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