Polytope of Type {2,52,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,52,6}*1248a
if this polytope has a name.
Group : SmallGroup(1248,1320)
Rank : 4
Schlafli Type : {2,52,6}
Number of vertices, edges, etc : 2, 52, 156, 6
Order of s₀s₁s₂s₃ : 156
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) :
   2-fold quotients : {2,26,6}*624
   3-fold quotients : {2,52,2}*416
   6-fold quotients : {2,26,2}*208
   12-fold quotients : {2,13,2}*104
   13-fold quotients : {2,4,6}*96a
   26-fold quotients : {2,2,6}*48
   39-fold quotients : {2,4,2}*32
   52-fold quotients : {2,2,3}*24
   78-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)
( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81,120)( 82,132)( 83,131)( 84,130)
( 85,129)( 86,128)( 87,127)( 88,126)( 89,125)( 90,124)( 91,123)( 92,122)
( 93,121)( 94,133)( 95,145)( 96,144)( 97,143)( 98,142)( 99,141)(100,140)
(101,139)(102,138)(103,137)(104,136)(105,135)(106,134)(107,146)(108,158)
(109,157)(110,156)(111,155)(112,154)(113,153)(114,152)(115,151)(116,150)
(117,149)(118,148)(119,147);;
s2 := (  3, 82)(  4, 81)(  5, 93)(  6, 92)(  7, 91)(  8, 90)(  9, 89)( 10, 88)
( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16,108)( 17,107)( 18,119)
( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)( 26,111)
( 27,110)( 28,109)( 29, 95)( 30, 94)( 31,106)( 32,105)( 33,104)( 34,103)
( 35,102)( 36,101)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)( 42,121)
( 43,120)( 44,132)( 45,131)( 46,130)( 47,129)( 48,128)( 49,127)( 50,126)
( 51,125)( 52,124)( 53,123)( 54,122)( 55,147)( 56,146)( 57,158)( 58,157)
( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)
( 67,148)( 68,134)( 69,133)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)
( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135);;
s3 := (  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)(  9, 22)( 10, 23)
( 11, 24)( 12, 25)( 13, 26)( 14, 27)( 15, 28)( 42, 55)( 43, 56)( 44, 57)
( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)
( 53, 66)( 54, 67)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)
( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)( 92,105)( 93,106)(120,133)
(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)
(129,142)(130,143)(131,144)(132,145);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(158)!(1,2);
s1 := Sym(158)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81,120)( 82,132)( 83,131)
( 84,130)( 85,129)( 86,128)( 87,127)( 88,126)( 89,125)( 90,124)( 91,123)
( 92,122)( 93,121)( 94,133)( 95,145)( 96,144)( 97,143)( 98,142)( 99,141)
(100,140)(101,139)(102,138)(103,137)(104,136)(105,135)(106,134)(107,146)
(108,158)(109,157)(110,156)(111,155)(112,154)(113,153)(114,152)(115,151)
(116,150)(117,149)(118,148)(119,147);
s2 := Sym(158)!(  3, 82)(  4, 81)(  5, 93)(  6, 92)(  7, 91)(  8, 90)(  9, 89)
( 10, 88)( 11, 87)( 12, 86)( 13, 85)( 14, 84)( 15, 83)( 16,108)( 17,107)
( 18,119)( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)
( 26,111)( 27,110)( 28,109)( 29, 95)( 30, 94)( 31,106)( 32,105)( 33,104)
( 34,103)( 35,102)( 36,101)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)
( 42,121)( 43,120)( 44,132)( 45,131)( 46,130)( 47,129)( 48,128)( 49,127)
( 50,126)( 51,125)( 52,124)( 53,123)( 54,122)( 55,147)( 56,146)( 57,158)
( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)
( 66,149)( 67,148)( 68,134)( 69,133)( 70,145)( 71,144)( 72,143)( 73,142)
( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135);
s3 := Sym(158)!(  3, 16)(  4, 17)(  5, 18)(  6, 19)(  7, 20)(  8, 21)(  9, 22)
( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 14, 27)( 15, 28)( 42, 55)( 43, 56)
( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)
( 52, 65)( 53, 66)( 54, 67)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)
( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)( 92,105)( 93,106)
(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)
(128,141)(129,142)(130,143)(131,144)(132,145);
poly := sub<Sym(158)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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