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Polytope of Type {6,51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,51}*1836
if this polytope has a name.
Group : SmallGroup(1836,53)
Rank : 3
Schlafli Type : {6,51}
Number of vertices, edges, etc : 18, 459, 153
Order of s0s1s2 : 102
Order of s0s1s2s1 : 6
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 : {6,51}*612
   9-fold quotients : {2,51}*204
   17-fold quotients : {6,3}*108
   27-fold quotients : {2,17}*68
   51-fold quotients : {6,3}*36
   153-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)
( 50, 51)( 52,103)( 53,105)( 54,104)( 55,106)( 56,108)( 57,107)( 58,109)
( 59,111)( 60,110)( 61,112)( 62,114)( 63,113)( 64,115)( 65,117)( 66,116)
( 67,118)( 68,120)( 69,119)( 70,121)( 71,123)( 72,122)( 73,124)( 74,126)
( 75,125)( 76,127)( 77,129)( 78,128)( 79,130)( 80,132)( 81,131)( 82,133)
( 83,135)( 84,134)( 85,136)( 86,138)( 87,137)( 88,139)( 89,141)( 90,140)
( 91,142)( 92,144)( 93,143)( 94,145)( 95,147)( 96,146)( 97,148)( 98,150)
( 99,149)(100,151)(101,153)(102,152);;
s1 := (  1, 52)(  2, 53)(  3, 54)(  4,100)(  5,101)(  6,102)(  7, 97)(  8, 98)
(  9, 99)( 10, 94)( 11, 95)( 12, 96)( 13, 91)( 14, 92)( 15, 93)( 16, 88)
( 17, 89)( 18, 90)( 19, 85)( 20, 86)( 21, 87)( 22, 82)( 23, 83)( 24, 84)
( 25, 79)( 26, 80)( 27, 81)( 28, 76)( 29, 77)( 30, 78)( 31, 73)( 32, 74)
( 33, 75)( 34, 70)( 35, 71)( 36, 72)( 37, 67)( 38, 68)( 39, 69)( 40, 64)
( 41, 65)( 42, 66)( 43, 61)( 44, 62)( 45, 63)( 46, 58)( 47, 59)( 48, 60)
( 49, 55)( 50, 56)( 51, 57)(106,151)(107,152)(108,153)(109,148)(110,149)
(111,150)(112,145)(113,146)(114,147)(115,142)(116,143)(117,144)(118,139)
(119,140)(120,141)(121,136)(122,137)(123,138)(124,133)(125,134)(126,135)
(127,130)(128,131)(129,132);;
s2 := (  1,  4)(  2,  5)(  3,  6)(  7, 49)(  8, 50)(  9, 51)( 10, 46)( 11, 47)
( 12, 48)( 13, 43)( 14, 44)( 15, 45)( 16, 40)( 17, 41)( 18, 42)( 19, 37)
( 20, 38)( 21, 39)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)( 27, 33)
( 52,108)( 53,106)( 54,107)( 55,105)( 56,103)( 57,104)( 58,153)( 59,151)
( 60,152)( 61,150)( 62,148)( 63,149)( 64,147)( 65,145)( 66,146)( 67,144)
( 68,142)( 69,143)( 70,141)( 71,139)( 72,140)( 73,138)( 74,136)( 75,137)
( 76,135)( 77,133)( 78,134)( 79,132)( 80,130)( 81,131)( 82,129)( 83,127)
( 84,128)( 85,126)( 86,124)( 87,125)( 88,123)( 89,121)( 90,122)( 91,120)
( 92,118)( 93,119)( 94,117)( 95,115)( 96,116)( 97,114)( 98,112)( 99,113)
(100,111)(101,109)(102,110);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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)!(  2,  3)(  5,  6)(  8,  9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)
( 47, 48)( 50, 51)( 52,103)( 53,105)( 54,104)( 55,106)( 56,108)( 57,107)
( 58,109)( 59,111)( 60,110)( 61,112)( 62,114)( 63,113)( 64,115)( 65,117)
( 66,116)( 67,118)( 68,120)( 69,119)( 70,121)( 71,123)( 72,122)( 73,124)
( 74,126)( 75,125)( 76,127)( 77,129)( 78,128)( 79,130)( 80,132)( 81,131)
( 82,133)( 83,135)( 84,134)( 85,136)( 86,138)( 87,137)( 88,139)( 89,141)
( 90,140)( 91,142)( 92,144)( 93,143)( 94,145)( 95,147)( 96,146)( 97,148)
( 98,150)( 99,149)(100,151)(101,153)(102,152);
s1 := Sym(153)!(  1, 52)(  2, 53)(  3, 54)(  4,100)(  5,101)(  6,102)(  7, 97)
(  8, 98)(  9, 99)( 10, 94)( 11, 95)( 12, 96)( 13, 91)( 14, 92)( 15, 93)
( 16, 88)( 17, 89)( 18, 90)( 19, 85)( 20, 86)( 21, 87)( 22, 82)( 23, 83)
( 24, 84)( 25, 79)( 26, 80)( 27, 81)( 28, 76)( 29, 77)( 30, 78)( 31, 73)
( 32, 74)( 33, 75)( 34, 70)( 35, 71)( 36, 72)( 37, 67)( 38, 68)( 39, 69)
( 40, 64)( 41, 65)( 42, 66)( 43, 61)( 44, 62)( 45, 63)( 46, 58)( 47, 59)
( 48, 60)( 49, 55)( 50, 56)( 51, 57)(106,151)(107,152)(108,153)(109,148)
(110,149)(111,150)(112,145)(113,146)(114,147)(115,142)(116,143)(117,144)
(118,139)(119,140)(120,141)(121,136)(122,137)(123,138)(124,133)(125,134)
(126,135)(127,130)(128,131)(129,132);
s2 := Sym(153)!(  1,  4)(  2,  5)(  3,  6)(  7, 49)(  8, 50)(  9, 51)( 10, 46)
( 11, 47)( 12, 48)( 13, 43)( 14, 44)( 15, 45)( 16, 40)( 17, 41)( 18, 42)
( 19, 37)( 20, 38)( 21, 39)( 22, 34)( 23, 35)( 24, 36)( 25, 31)( 26, 32)
( 27, 33)( 52,108)( 53,106)( 54,107)( 55,105)( 56,103)( 57,104)( 58,153)
( 59,151)( 60,152)( 61,150)( 62,148)( 63,149)( 64,147)( 65,145)( 66,146)
( 67,144)( 68,142)( 69,143)( 70,141)( 71,139)( 72,140)( 73,138)( 74,136)
( 75,137)( 76,135)( 77,133)( 78,134)( 79,132)( 80,130)( 81,131)( 82,129)
( 83,127)( 84,128)( 85,126)( 86,124)( 87,125)( 88,123)( 89,121)( 90,122)
( 91,120)( 92,118)( 93,119)( 94,117)( 95,115)( 96,116)( 97,114)( 98,112)
( 99,113)(100,111)(101,109)(102,110);
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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*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