Polytope of Type {4,74} with group SmallGroup(592,39)

Overview

Group: SmallGroup(592,39)
Rank: 3
Schläfli Type: {4,74}
Vertices, edges, …: 4, 148, 74
Order of s₀s₁s₂: 148
Order of s₀s₁s₂s₁: 2
Also known as: {4,74|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{2,74}*296

4-fold

{2,37}*148

37-fold

{4,2}*16

74-fold

{2,2}*8

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References