Polytope of Type {39,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39,12}*1872
if this polytope has a name.
Group : SmallGroup(1872,1036)
Rank : 3
Schlafli Type : {39,12}
Number of vertices, edges, etc : 78, 468, 24
Order of s₀s₁s₂ : 78
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {39,4}*624
   4-fold quotients : {39,6}*468
   6-fold quotients : {39,4}*312
   12-fold quotients : {39,2}*156
   13-fold quotients : {3,12}*144
   36-fold quotients : {13,2}*52
   39-fold quotients : {3,4}*48
   52-fold quotients : {3,6}*36
   78-fold quotients : {3,4}*24
   156-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope