Polytope of Type {76,4} with group SmallGroup(1216,737)

Overview

Group: SmallGroup(1216,737)
Rank: 3
Schläfli Type: {76,4}
Vertices, edges, …: 152, 304, 8
Order of s₀s₁s₂: 76
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

{76,4}*608

4-fold

8-fold

{38,2}*152

16-fold

{19,2}*76

19-fold

{4,4}*64

38-fold

{4,4}*32

76-fold

152-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s1*s2)^2> of order 2

4 facets

4 of {76}*152

114 vertex figures

76 of {2}*4
38 of {4}*8

P/N, where N=<(s0*s1)^38> of order 2

6 facets

4 of {38}*76
2 of {76}*152

76 vertex figures

76 of {4}*8

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.