Polytope of Type {38,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,6}*456
Also Known As : {38,6|2}. if this polytope has another name.
Group : SmallGroup(456,47)
Rank : 3
Schlafli Type : {38,6}
Number of vertices, edges, etc : 38, 114, 6
Order of s₀s₁s₂ : 114
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {38,6,2} of size 912
   {38,6,3} of size 1368
   {38,6,4} of size 1824
   {38,6,3} of size 1824
   {38,6,4} of size 1824
Vertex Figure Of :
   {2,38,6} of size 912
   {4,38,6} of size 1824
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {38,2}*152
   6-fold quotients : {19,2}*76
   19-fold quotients : {2,6}*24
   38-fold quotients : {2,3}*12
   57-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {38,12}*912, {76,6}*912a
   3-fold covers : {38,18}*1368, {114,6}*1368a, {114,6}*1368b
   4-fold covers : {38,24}*1824, {152,6}*1824, {76,12}*1824, {76,6}*1824
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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