Polytope of Type {2,76,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,76,4}*1216
if this polytope has a name.
Group : SmallGroup(1216,1036)
Rank : 4
Schlafli Type : {2,76,4}
Number of vertices, edges, etc : 2, 76, 152, 4
Order of s₀s₁s₂s₃ : 76
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 : {2,76,2}*608, {2,38,4}*608
   4-fold quotients : {2,38,2}*304
   8-fold quotients : {2,19,2}*152
   19-fold quotients : {2,4,4}*64
   38-fold quotients : {2,2,4}*32, {2,4,2}*32
   76-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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