Polytope of Type {6,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,51}*612
if this polytope has a name.
Group : SmallGroup(612,28)
Rank : 3
Schlafli Type : {6,51}
Number of vertices, edges, etc : 6, 153, 51
Order of s₀s₁s₂ : 102
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,51,2} of size 1224
Vertex Figure Of :
   {2,6,51} of size 1224
   {3,6,51} of size 1836
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,51}*204
   9-fold quotients : {2,17}*68
   17-fold quotients : {6,3}*36
   51-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,102}*1224c
   3-fold covers : {6,153}*1836, {6,51}*1836
Permutation Representation (GAP) :

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