Polytope of Type {48,6} with group SmallGroup(576,2112)

Overview

Group: SmallGroup(576,2112)
Rank: 3
Schläfli Type: {48,6}
Vertices, edges, …: 48, 144, 6
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 2
Also known as: {48,6|2}. if this polytope has another name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{24,6}*288a

3-fold

4-fold

{12,6}*144a

6-fold

8-fold

{6,6}*72a

9-fold

{16,2}*64

12-fold

18-fold

{8,2}*32

24-fold

36-fold

{4,2}*16

48-fold

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