Polytope of Type {51,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {51,6,3}*1836
if this polytope has a name.
Group : SmallGroup(1836,53)
Rank : 4
Schlafli Type : {51,6,3}
Number of vertices, edges, etc : 51, 153, 9, 3
Order of s₀s₁s₂s₃ : 51
Order of s₀s₁s₂s₃s₂s₁ : 6
Special Properties :
   Universal
   Orientable
   Flat
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 : {51,2,3}*612
   9-fold quotients : {17,2,3}*204
   17-fold quotients : {3,6,3}*108
   51-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 49)(  5, 51)(  6, 50)(  7, 46)(  8, 48)(  9, 47)( 10, 43)
( 11, 45)( 12, 44)( 13, 40)( 14, 42)( 15, 41)( 16, 37)( 17, 39)( 18, 38)
( 19, 34)( 20, 36)( 21, 35)( 22, 31)( 23, 33)( 24, 32)( 25, 28)( 26, 30)
( 27, 29)( 53, 54)( 55,100)( 56,102)( 57,101)( 58, 97)( 59, 99)( 60, 98)
( 61, 94)( 62, 96)( 63, 95)( 64, 91)( 65, 93)( 66, 92)( 67, 88)( 68, 90)
( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73, 82)( 74, 84)( 75, 83)( 76, 79)
( 77, 81)( 78, 80)(104,105)(106,151)(107,153)(108,152)(109,148)(110,150)
(111,149)(112,145)(113,147)(114,146)(115,142)(116,144)(117,143)(118,139)
(119,141)(120,140)(121,136)(122,138)(123,137)(124,133)(125,135)(126,134)
(127,130)(128,132)(129,131);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7, 49)(  8, 51)(  9, 50)( 10, 46)( 11, 48)
( 12, 47)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)( 19, 37)
( 20, 39)( 21, 38)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)
( 29, 30)( 52, 56)( 53, 55)( 54, 57)( 58,101)( 59,100)( 60,102)( 61, 98)
( 62, 97)( 63, 99)( 64, 95)( 65, 94)( 66, 96)( 67, 92)( 68, 91)( 69, 93)
( 70, 89)( 71, 88)( 72, 90)( 73, 86)( 74, 85)( 75, 87)( 76, 83)( 77, 82)
( 78, 84)( 79, 80)(103,108)(104,107)(105,106)(109,153)(110,152)(111,151)
(112,150)(113,149)(114,148)(115,147)(116,146)(117,145)(118,144)(119,143)
(120,142)(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)(127,135)
(128,134)(129,133)(130,132);;
s2 := (  1, 52)(  2, 54)(  3, 53)(  4, 55)(  5, 57)(  6, 56)(  7, 58)(  8, 60)
(  9, 59)( 10, 61)( 11, 63)( 12, 62)( 13, 64)( 14, 66)( 15, 65)( 16, 67)
( 17, 69)( 18, 68)( 19, 70)( 20, 72)( 21, 71)( 22, 73)( 23, 75)( 24, 74)
( 25, 76)( 26, 78)( 27, 77)( 28, 79)( 29, 81)( 30, 80)( 31, 82)( 32, 84)
( 33, 83)( 34, 85)( 35, 87)( 36, 86)( 37, 88)( 38, 90)( 39, 89)( 40, 91)
( 41, 93)( 42, 92)( 43, 94)( 44, 96)( 45, 95)( 46, 97)( 47, 99)( 48, 98)
( 49,100)( 50,102)( 51,101)(104,105)(107,108)(110,111)(113,114)(116,117)
(119,120)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)(140,141)
(143,144)(146,147)(149,150)(152,153);;
s3 := (  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);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
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*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(153)!(  2,  3)(  4, 49)(  5, 51)(  6, 50)(  7, 46)(  8, 48)(  9, 47)
( 10, 43)( 11, 45)( 12, 44)( 13, 40)( 14, 42)( 15, 41)( 16, 37)( 17, 39)
( 18, 38)( 19, 34)( 20, 36)( 21, 35)( 22, 31)( 23, 33)( 24, 32)( 25, 28)
( 26, 30)( 27, 29)( 53, 54)( 55,100)( 56,102)( 57,101)( 58, 97)( 59, 99)
( 60, 98)( 61, 94)( 62, 96)( 63, 95)( 64, 91)( 65, 93)( 66, 92)( 67, 88)
( 68, 90)( 69, 89)( 70, 85)( 71, 87)( 72, 86)( 73, 82)( 74, 84)( 75, 83)
( 76, 79)( 77, 81)( 78, 80)(104,105)(106,151)(107,153)(108,152)(109,148)
(110,150)(111,149)(112,145)(113,147)(114,146)(115,142)(116,144)(117,143)
(118,139)(119,141)(120,140)(121,136)(122,138)(123,137)(124,133)(125,135)
(126,134)(127,130)(128,132)(129,131);
s1 := Sym(153)!(  1,  4)(  2,  6)(  3,  5)(  7, 49)(  8, 51)(  9, 50)( 10, 46)
( 11, 48)( 12, 47)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)
( 19, 37)( 20, 39)( 21, 38)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)
( 27, 32)( 29, 30)( 52, 56)( 53, 55)( 54, 57)( 58,101)( 59,100)( 60,102)
( 61, 98)( 62, 97)( 63, 99)( 64, 95)( 65, 94)( 66, 96)( 67, 92)( 68, 91)
( 69, 93)( 70, 89)( 71, 88)( 72, 90)( 73, 86)( 74, 85)( 75, 87)( 76, 83)
( 77, 82)( 78, 84)( 79, 80)(103,108)(104,107)(105,106)(109,153)(110,152)
(111,151)(112,150)(113,149)(114,148)(115,147)(116,146)(117,145)(118,144)
(119,143)(120,142)(121,141)(122,140)(123,139)(124,138)(125,137)(126,136)
(127,135)(128,134)(129,133)(130,132);
s2 := Sym(153)!(  1, 52)(  2, 54)(  3, 53)(  4, 55)(  5, 57)(  6, 56)(  7, 58)
(  8, 60)(  9, 59)( 10, 61)( 11, 63)( 12, 62)( 13, 64)( 14, 66)( 15, 65)
( 16, 67)( 17, 69)( 18, 68)( 19, 70)( 20, 72)( 21, 71)( 22, 73)( 23, 75)
( 24, 74)( 25, 76)( 26, 78)( 27, 77)( 28, 79)( 29, 81)( 30, 80)( 31, 82)
( 32, 84)( 33, 83)( 34, 85)( 35, 87)( 36, 86)( 37, 88)( 38, 90)( 39, 89)
( 40, 91)( 41, 93)( 42, 92)( 43, 94)( 44, 96)( 45, 95)( 46, 97)( 47, 99)
( 48, 98)( 49,100)( 50,102)( 51,101)(104,105)(107,108)(110,111)(113,114)
(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)(134,135)(137,138)
(140,141)(143,144)(146,147)(149,150)(152,153);
s3 := 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);
poly := sub<Sym(153)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 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*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