Polytope of Type {2,51,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,51,6}*1224
if this polytope has a name.
Group : SmallGroup(1224,156)
Rank : 4
Schlafli Type : {2,51,6}
Number of vertices, edges, etc : 2, 51, 153, 6
Order of s₀s₁s₂s₃ : 102
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,51,2}*408
   9-fold quotients : {2,17,2}*136
   17-fold quotients : {2,3,6}*72
   51-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)( 11, 12)
( 20, 37)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)( 27, 47)
( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)( 35, 39)
( 36, 38)( 54,105)( 55,121)( 56,120)( 57,119)( 58,118)( 59,117)( 60,116)
( 61,115)( 62,114)( 63,113)( 64,112)( 65,111)( 66,110)( 67,109)( 68,108)
( 69,107)( 70,106)( 71,139)( 72,155)( 73,154)( 74,153)( 75,152)( 76,151)
( 77,150)( 78,149)( 79,148)( 80,147)( 81,146)( 82,145)( 83,144)( 84,143)
( 85,142)( 86,141)( 87,140)( 88,122)( 89,138)( 90,137)( 91,136)( 92,135)
( 93,134)( 94,133)( 95,132)( 96,131)( 97,130)( 98,129)( 99,128)(100,127)
(101,126)(102,125)(103,124)(104,123);;
s2 := (  3, 72)(  4, 71)(  5, 87)(  6, 86)(  7, 85)(  8, 84)(  9, 83)( 10, 82)
( 11, 81)( 12, 80)( 13, 79)( 14, 78)( 15, 77)( 16, 76)( 17, 75)( 18, 74)
( 19, 73)( 20, 55)( 21, 54)( 22, 70)( 23, 69)( 24, 68)( 25, 67)( 26, 66)
( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 61)( 32, 60)( 33, 59)( 34, 58)
( 35, 57)( 36, 56)( 37, 89)( 38, 88)( 39,104)( 40,103)( 41,102)( 42,101)
( 43,100)( 44, 99)( 45, 98)( 46, 97)( 47, 96)( 48, 95)( 49, 94)( 50, 93)
( 51, 92)( 52, 91)( 53, 90)(105,123)(106,122)(107,138)(108,137)(109,136)
(110,135)(111,134)(112,133)(113,132)(114,131)(115,130)(116,129)(117,128)
(118,127)(119,126)(120,125)(121,124)(139,140)(141,155)(142,154)(143,153)
(144,152)(145,151)(146,150)(147,149);;
s3 := ( 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)(103,154)(104,155);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(155)!(1,2);
s1 := Sym(155)!(  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)
( 11, 12)( 20, 37)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)
( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)
( 35, 39)( 36, 38)( 54,105)( 55,121)( 56,120)( 57,119)( 58,118)( 59,117)
( 60,116)( 61,115)( 62,114)( 63,113)( 64,112)( 65,111)( 66,110)( 67,109)
( 68,108)( 69,107)( 70,106)( 71,139)( 72,155)( 73,154)( 74,153)( 75,152)
( 76,151)( 77,150)( 78,149)( 79,148)( 80,147)( 81,146)( 82,145)( 83,144)
( 84,143)( 85,142)( 86,141)( 87,140)( 88,122)( 89,138)( 90,137)( 91,136)
( 92,135)( 93,134)( 94,133)( 95,132)( 96,131)( 97,130)( 98,129)( 99,128)
(100,127)(101,126)(102,125)(103,124)(104,123);
s2 := Sym(155)!(  3, 72)(  4, 71)(  5, 87)(  6, 86)(  7, 85)(  8, 84)(  9, 83)
( 10, 82)( 11, 81)( 12, 80)( 13, 79)( 14, 78)( 15, 77)( 16, 76)( 17, 75)
( 18, 74)( 19, 73)( 20, 55)( 21, 54)( 22, 70)( 23, 69)( 24, 68)( 25, 67)
( 26, 66)( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 61)( 32, 60)( 33, 59)
( 34, 58)( 35, 57)( 36, 56)( 37, 89)( 38, 88)( 39,104)( 40,103)( 41,102)
( 42,101)( 43,100)( 44, 99)( 45, 98)( 46, 97)( 47, 96)( 48, 95)( 49, 94)
( 50, 93)( 51, 92)( 52, 91)( 53, 90)(105,123)(106,122)(107,138)(108,137)
(109,136)(110,135)(111,134)(112,133)(113,132)(114,131)(115,130)(116,129)
(117,128)(118,127)(119,126)(120,125)(121,124)(139,140)(141,155)(142,154)
(143,153)(144,152)(145,151)(146,150)(147,149);
s3 := Sym(155)!( 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)(103,154)(104,155);
poly := sub<Sym(155)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2*s1*s2 >;

to this polytope