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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,38,6,2}*1824
if this polytope has a name.
Group : SmallGroup(1824,1255)
Rank : 5
Schlafli Type : {2,38,6,2}
Number of vertices, edges, etc : 2, 38, 114, 6, 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 : {2,2,6,2}*96
   38-fold quotients : {2,2,3,2}*48
   57-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)( 11, 14)
( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)
( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)( 47, 54)
( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)( 83, 94)
( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)(101,114)
(102,113)(103,112)(104,111)(105,110)(106,109)(107,108);;
s2 := (  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)( 11, 15)
( 12, 14)( 22, 42)( 23, 41)( 24, 59)( 25, 58)( 26, 57)( 27, 56)( 28, 55)
( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)( 36, 47)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 60, 61)( 62, 78)( 63, 77)( 64, 76)
( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 99)( 80, 98)( 81,116)
( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)( 89,108)
( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100);;
s3 := (  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 83)(  8, 84)(  9, 85)( 10, 86)
( 11, 87)( 12, 88)( 13, 89)( 14, 90)( 15, 91)( 16, 92)( 17, 93)( 18, 94)
( 19, 95)( 20, 96)( 21, 97)( 22, 60)( 23, 61)( 24, 62)( 25, 63)( 26, 64)
( 27, 65)( 28, 66)( 29, 67)( 30, 68)( 31, 69)( 32, 70)( 33, 71)( 34, 72)
( 35, 73)( 36, 74)( 37, 75)( 38, 76)( 39, 77)( 40, 78)( 41, 98)( 42, 99)
( 43,100)( 44,101)( 45,102)( 46,103)( 47,104)( 48,105)( 49,106)( 50,107)
( 51,108)( 52,109)( 53,110)( 54,111)( 55,112)( 56,113)( 57,114)( 58,115)
( 59,116);;
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*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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*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*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)!(1,2);
s1 := Sym(118)!(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)( 10, 15)
( 11, 14)( 12, 13)( 23, 40)( 24, 39)( 25, 38)( 26, 37)( 27, 36)( 28, 35)
( 29, 34)( 30, 33)( 31, 32)( 42, 59)( 43, 58)( 44, 57)( 45, 56)( 46, 55)
( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)( 80, 97)( 81, 96)( 82, 95)
( 83, 94)( 84, 93)( 85, 92)( 86, 91)( 87, 90)( 88, 89)( 99,116)(100,115)
(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108);
s2 := Sym(118)!(  3,  4)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)( 10, 16)
( 11, 15)( 12, 14)( 22, 42)( 23, 41)( 24, 59)( 25, 58)( 26, 57)( 27, 56)
( 28, 55)( 29, 54)( 30, 53)( 31, 52)( 32, 51)( 33, 50)( 34, 49)( 35, 48)
( 36, 47)( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 60, 61)( 62, 78)( 63, 77)
( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)( 69, 71)( 79, 99)( 80, 98)
( 81,116)( 82,115)( 83,114)( 84,113)( 85,112)( 86,111)( 87,110)( 88,109)
( 89,108)( 90,107)( 91,106)( 92,105)( 93,104)( 94,103)( 95,102)( 96,101)
( 97,100);
s3 := Sym(118)!(  3, 79)(  4, 80)(  5, 81)(  6, 82)(  7, 83)(  8, 84)(  9, 85)
( 10, 86)( 11, 87)( 12, 88)( 13, 89)( 14, 90)( 15, 91)( 16, 92)( 17, 93)
( 18, 94)( 19, 95)( 20, 96)( 21, 97)( 22, 60)( 23, 61)( 24, 62)( 25, 63)
( 26, 64)( 27, 65)( 28, 66)( 29, 67)( 30, 68)( 31, 69)( 32, 70)( 33, 71)
( 34, 72)( 35, 73)( 36, 74)( 37, 75)( 38, 76)( 39, 77)( 40, 78)( 41, 98)
( 42, 99)( 43,100)( 44,101)( 45,102)( 46,103)( 47,104)( 48,105)( 49,106)
( 50,107)( 51,108)( 52,109)( 53,110)( 54,111)( 55,112)( 56,113)( 57,114)
( 58,115)( 59,116);
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*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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope