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

Overview

Group: SmallGroup(1216,737)
Rank: 3
Schläfli Type: {4,76}
Vertices, edges, …: 8, 304, 152
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

Quotients maximal quotients in bold

2-fold

{4,76}*608

4-fold

8-fold

{2,38}*152

16-fold

{2,19}*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=<(s0*s1)^2> of order 2

114 facets

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

4 vertex figures

4 of {76}*152

P/N, where N=<(s1*s2)^38> of order 2

76 facets

76 of {4}*8

6 vertex figures

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

Representations

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, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 
s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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.