Polytope of Type {156,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {156,6}*1872d
if this polytope has a name.
Group : SmallGroup(1872,1037)
Rank : 3
Schlafli Type : {156,6}
Number of vertices, edges, etc : 156, 468, 6
Order of s₀s₁s₂ : 39
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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 : {52,6}*624b
   13-fold quotients : {12,6}*144d
   39-fold quotients : {4,6}*48b
   78-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope