Polytope of Type {4,76}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,76}*1216
if this polytope has a name.
Group : SmallGroup(1216,737)
Rank : 3
Schlafli Type : {4,76}
Number of vertices, edges, etc : 8, 304, 152
Order of s₀s₁s₂ : 76
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,76}*608
   4-fold quotients : {2,76}*304, {4,38}*304
   8-fold quotients : {2,38}*152
   16-fold quotients : {2,19}*76
   19-fold quotients : {4,4}*64
   38-fold quotients : {4,4}*32
   76-fold quotients : {2,4}*16, {4,2}*16
   152-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope