Polytope of Type {51,6}

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

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