Questions?
See the FAQ
or other info.

Polytope of Type {12,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,39}*1872
if this polytope has a name.
Group : SmallGroup(1872,1036)
Rank : 3
Schlafli Type : {12,39}
Number of vertices, edges, etc : 24, 468, 78
Order of s0s1s2 : 78
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,39}*624
   4-fold quotients : {6,39}*468
   6-fold quotients : {4,39}*312
   12-fold quotients : {2,39}*156
   13-fold quotients : {12,3}*144
   36-fold quotients : {2,13}*52
   39-fold quotients : {4,3}*48
   52-fold quotients : {6,3}*36
   78-fold quotients : {4,3}*24
   156-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53,107)( 54,108)( 55,105)( 56,106)( 57,111)( 58,112)
( 59,109)( 60,110)( 61,115)( 62,116)( 63,113)( 64,114)( 65,119)( 66,120)
( 67,117)( 68,118)( 69,123)( 70,124)( 71,121)( 72,122)( 73,127)( 74,128)
( 75,125)( 76,126)( 77,131)( 78,132)( 79,129)( 80,130)( 81,135)( 82,136)
( 83,133)( 84,134)( 85,139)( 86,140)( 87,137)( 88,138)( 89,143)( 90,144)
( 91,141)( 92,142)( 93,147)( 94,148)( 95,145)( 96,146)( 97,151)( 98,152)
( 99,149)(100,150)(101,155)(102,156)(103,153)(104,154);;
s1 := (  1, 53)(  2, 54)(  3, 56)(  4, 55)(  5,101)(  6,102)(  7,104)(  8,103)
(  9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)( 16, 95)
( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 85)( 22, 86)( 23, 88)( 24, 87)
( 25, 81)( 26, 82)( 27, 84)( 28, 83)( 29, 77)( 30, 78)( 31, 80)( 32, 79)
( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)( 40, 71)
( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 61)( 46, 62)( 47, 64)( 48, 63)
( 49, 57)( 50, 58)( 51, 60)( 52, 59)(107,108)(109,153)(110,154)(111,156)
(112,155)(113,149)(114,150)(115,152)(116,151)(117,145)(118,146)(119,148)
(120,147)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)(127,140)
(128,139)(129,133)(130,134)(131,136)(132,135);;
s2 := (  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9, 49)( 10, 52)( 11, 51)( 12, 50)
( 13, 45)( 14, 48)( 15, 47)( 16, 46)( 17, 41)( 18, 44)( 19, 43)( 20, 42)
( 21, 37)( 22, 40)( 23, 39)( 24, 38)( 25, 33)( 26, 36)( 27, 35)( 28, 34)
( 30, 32)( 53,109)( 54,112)( 55,111)( 56,110)( 57,105)( 58,108)( 59,107)
( 60,106)( 61,153)( 62,156)( 63,155)( 64,154)( 65,149)( 66,152)( 67,151)
( 68,150)( 69,145)( 70,148)( 71,147)( 72,146)( 73,141)( 74,144)( 75,143)
( 76,142)( 77,137)( 78,140)( 79,139)( 80,138)( 81,133)( 82,136)( 83,135)
( 84,134)( 85,129)( 86,132)( 87,131)( 88,130)( 89,125)( 90,128)( 91,127)
( 92,126)( 93,121)( 94,124)( 95,123)( 96,122)( 97,117)( 98,120)( 99,119)
(100,118)(101,113)(102,116)(103,115)(104,114);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(156)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53,107)( 54,108)( 55,105)( 56,106)( 57,111)
( 58,112)( 59,109)( 60,110)( 61,115)( 62,116)( 63,113)( 64,114)( 65,119)
( 66,120)( 67,117)( 68,118)( 69,123)( 70,124)( 71,121)( 72,122)( 73,127)
( 74,128)( 75,125)( 76,126)( 77,131)( 78,132)( 79,129)( 80,130)( 81,135)
( 82,136)( 83,133)( 84,134)( 85,139)( 86,140)( 87,137)( 88,138)( 89,143)
( 90,144)( 91,141)( 92,142)( 93,147)( 94,148)( 95,145)( 96,146)( 97,151)
( 98,152)( 99,149)(100,150)(101,155)(102,156)(103,153)(104,154);
s1 := Sym(156)!(  1, 53)(  2, 54)(  3, 56)(  4, 55)(  5,101)(  6,102)(  7,104)
(  8,103)(  9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)
( 16, 95)( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 85)( 22, 86)( 23, 88)
( 24, 87)( 25, 81)( 26, 82)( 27, 84)( 28, 83)( 29, 77)( 30, 78)( 31, 80)
( 32, 79)( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)
( 40, 71)( 41, 65)( 42, 66)( 43, 68)( 44, 67)( 45, 61)( 46, 62)( 47, 64)
( 48, 63)( 49, 57)( 50, 58)( 51, 60)( 52, 59)(107,108)(109,153)(110,154)
(111,156)(112,155)(113,149)(114,150)(115,152)(116,151)(117,145)(118,146)
(119,148)(120,147)(121,141)(122,142)(123,144)(124,143)(125,137)(126,138)
(127,140)(128,139)(129,133)(130,134)(131,136)(132,135);
s2 := Sym(156)!(  1,  5)(  2,  8)(  3,  7)(  4,  6)(  9, 49)( 10, 52)( 11, 51)
( 12, 50)( 13, 45)( 14, 48)( 15, 47)( 16, 46)( 17, 41)( 18, 44)( 19, 43)
( 20, 42)( 21, 37)( 22, 40)( 23, 39)( 24, 38)( 25, 33)( 26, 36)( 27, 35)
( 28, 34)( 30, 32)( 53,109)( 54,112)( 55,111)( 56,110)( 57,105)( 58,108)
( 59,107)( 60,106)( 61,153)( 62,156)( 63,155)( 64,154)( 65,149)( 66,152)
( 67,151)( 68,150)( 69,145)( 70,148)( 71,147)( 72,146)( 73,141)( 74,144)
( 75,143)( 76,142)( 77,137)( 78,140)( 79,139)( 80,138)( 81,133)( 82,136)
( 83,135)( 84,134)( 85,129)( 86,132)( 87,131)( 88,130)( 89,125)( 90,128)
( 91,127)( 92,126)( 93,121)( 94,124)( 95,123)( 96,122)( 97,117)( 98,120)
( 99,119)(100,118)(101,113)(102,116)(103,115)(104,114);
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*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*s1*s2 >; 
 
References : None.
to this polytope