Polytope of Type {6,38,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,38,2,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1255)
Rank : 5
Schlafli Type : {6,38,2,2}
Number of vertices, edges, etc : 6, 114, 38, 2, 2
Order of s0s1s2s3s4 : 114
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 : {2,38,2,2}*608
   6-fold quotients : {2,19,2,2}*304
   19-fold quotients : {6,2,2,2}*96
   38-fold quotients : {3,2,2,2}*48
   57-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)( 27, 46)
( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)( 35, 54)
( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)( 81,100)
( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)( 89,108)
( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114);;
s1 := (  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)(  8, 32)
(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)( 61, 93)
( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)( 69, 85)
( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 97,114)
( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106);;
s2 := (  1, 59)(  2, 58)(  3, 76)(  4, 75)(  5, 74)(  6, 73)(  7, 72)(  8, 71)
(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 64)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 78)( 21, 77)( 22, 95)( 23, 94)( 24, 93)
( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)
( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 97)( 40, 96)
( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)( 48,107)
( 49,106)( 50,105)( 51,104)( 52,103)( 53,102)( 54,101)( 55,100)( 56, 99)
( 57, 98);;
s3 := (115,116);;
s4 := (117,118);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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(118)!( 20, 39)( 21, 40)( 22, 41)( 23, 42)( 24, 43)( 25, 44)( 26, 45)
( 27, 46)( 28, 47)( 29, 48)( 30, 49)( 31, 50)( 32, 51)( 33, 52)( 34, 53)
( 35, 54)( 36, 55)( 37, 56)( 38, 57)( 77, 96)( 78, 97)( 79, 98)( 80, 99)
( 81,100)( 82,101)( 83,102)( 84,103)( 85,104)( 86,105)( 87,106)( 88,107)
( 89,108)( 90,109)( 91,110)( 92,111)( 93,112)( 94,113)( 95,114);
s1 := Sym(118)!(  1, 20)(  2, 38)(  3, 37)(  4, 36)(  5, 35)(  6, 34)(  7, 33)
(  8, 32)(  9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 40, 57)( 41, 56)( 42, 55)( 43, 54)
( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 58, 77)( 59, 95)( 60, 94)
( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)( 67, 87)( 68, 86)
( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)( 75, 79)( 76, 78)
( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)
(105,106);
s2 := Sym(118)!(  1, 59)(  2, 58)(  3, 76)(  4, 75)(  5, 74)(  6, 73)(  7, 72)
(  8, 71)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 64)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 78)( 21, 77)( 22, 95)( 23, 94)
( 24, 93)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)
( 32, 85)( 33, 84)( 34, 83)( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 97)
( 40, 96)( 41,114)( 42,113)( 43,112)( 44,111)( 45,110)( 46,109)( 47,108)
( 48,107)( 49,106)( 50,105)( 51,104)( 52,103)( 53,102)( 54,101)( 55,100)
( 56, 99)( 57, 98);
s3 := Sym(118)!(115,116);
s4 := Sym(118)!(117,118);
poly := sub<Sym(118)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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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