Polytope of Type {2,156,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,156,2}*1248
if this polytope has a name.
Group : SmallGroup(1248,1414)
Rank : 4
Schlafli Type : {2,156,2}
Number of vertices, edges, etc : 2, 156, 156, 2
Order of s₀s₁s₂s₃ : 156
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,78,2}*624
   3-fold quotients : {2,52,2}*416
   4-fold quotients : {2,39,2}*312
   6-fold quotients : {2,26,2}*208
   12-fold quotients : {2,13,2}*104
   13-fold quotients : {2,12,2}*96
   26-fold quotients : {2,6,2}*48
   39-fold quotients : {2,4,2}*32
   52-fold quotients : {2,3,2}*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)( 16, 29)( 17, 41)
( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 36)( 23, 35)( 24, 34)( 25, 33)
( 26, 32)( 27, 31)( 28, 30)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 55, 68)( 56, 80)( 57, 79)( 58, 78)( 59, 77)( 60, 76)( 61, 75)
( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 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)( 94,146)( 95,158)( 96,157)( 97,156)( 98,155)
( 99,154)(100,153)(101,152)(102,151)(103,150)(104,149)(105,148)(106,147)
(107,133)(108,145)(109,144)(110,143)(111,142)(112,141)(113,140)(114,139)
(115,138)(116,137)(117,136)(118,135)(119,134);;
s2 := (  3, 95)(  4, 94)(  5,106)(  6,105)(  7,104)(  8,103)(  9,102)( 10,101)
( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 82)( 17, 81)( 18, 93)
( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)( 26, 85)
( 27, 84)( 28, 83)( 29,108)( 30,107)( 31,119)( 32,118)( 33,117)( 34,116)
( 35,115)( 36,114)( 37,113)( 38,112)( 39,111)( 40,110)( 41,109)( 42,134)
( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)
( 51,138)( 52,137)( 53,136)( 54,135)( 55,121)( 56,120)( 57,132)( 58,131)
( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)( 66,123)
( 67,122)( 68,147)( 69,146)( 70,158)( 71,157)( 72,156)( 73,155)( 74,154)
( 75,153)( 76,152)( 77,151)( 78,150)( 79,149)( 80,148);;
s3 := (159,160);;
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, 
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*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*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(160)!(1,2);
s1 := Sym(160)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16, 29)
( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 36)( 23, 35)( 24, 34)
( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 43, 54)( 44, 53)( 45, 52)( 46, 51)
( 47, 50)( 48, 49)( 55, 68)( 56, 80)( 57, 79)( 58, 78)( 59, 77)( 60, 76)
( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)( 66, 70)( 67, 69)( 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)( 94,146)( 95,158)( 96,157)( 97,156)
( 98,155)( 99,154)(100,153)(101,152)(102,151)(103,150)(104,149)(105,148)
(106,147)(107,133)(108,145)(109,144)(110,143)(111,142)(112,141)(113,140)
(114,139)(115,138)(116,137)(117,136)(118,135)(119,134);
s2 := Sym(160)!(  3, 95)(  4, 94)(  5,106)(  6,105)(  7,104)(  8,103)(  9,102)
( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 82)( 17, 81)
( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29,108)( 30,107)( 31,119)( 32,118)( 33,117)
( 34,116)( 35,115)( 36,114)( 37,113)( 38,112)( 39,111)( 40,110)( 41,109)
( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)
( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,121)( 56,120)( 57,132)
( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)
( 66,123)( 67,122)( 68,147)( 69,146)( 70,158)( 71,157)( 72,156)( 73,155)
( 74,154)( 75,153)( 76,152)( 77,151)( 78,150)( 79,149)( 80,148);
s3 := Sym(160)!(159,160);
poly := sub<Sym(160)|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, 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*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*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 >;

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