Polytope of Type {6,48} with group SmallGroup(1920,240711)

Overview

Group: SmallGroup(1920,240711)
Rank: 3
Schläfli Type: {6,48}
Vertices, edges, …: 20, 480, 160
Order of s₀s₁s₂: 48
Order of s₀s₁s₂s₁: 20
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable

Quotients maximal quotients in bold

2-fold

{6,24}*960b

4-fold

{6,12}*480a

8-fold

{6,6}*240a

16-fold

{6,6}*120

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  2, 30)(  3, 34)(  7, 21)(  8, 43)(  9, 28)( 10, 12)( 11, 35)( 13, 44)( 14, 46)( 18, 27)( 19, 37)( 20, 38)( 22, 42)( 23, 29)( 24, 25)( 26, 45)( 31, 48)( 33, 41)( 36, 47)( 39, 40)( 50, 86)( 51, 62)( 55, 57)( 56, 95)( 58, 68)( 59, 75)( 60, 94)( 61, 79)( 66, 73)( 67, 70)( 69, 72)( 71, 84)( 74, 89)( 76, 83)( 77, 96)( 78, 82)( 81, 88)( 85, 87)( 90, 93)( 91, 92)( 97, 98)( 99,124)(100,104)(101,105)(102,106)(107,108)(109,138)(110,121)(111,118)(112,119)(113,120)(114,131)(122,125)(123,126)(127,136)(128,135)(129,141)(130,142)(137,139)(140,144)(145,165)(146,172)(148,181)(149,182)(150,151)(152,186)(153,156)(154,169)(159,191)(160,163)(161,164)(162,179)(166,173)(167,184)(168,174)(176,180)(177,189)(178,190)(183,187)(188,192);;
s1 := (  1,145)(  2,147)(  3,146)(  4,148)(  5,149)(  6,150)(  7,169)(  8,157)(  9,155)( 10,158)( 11,153)( 12,182)( 13,152)( 14,154)( 15,159)( 16,160)( 17,161)( 18,179)( 19,184)( 20,174)( 21,172)( 22,170)( 23,175)( 24,171)( 25,151)( 26,166)( 27,168)( 28,165)( 29,191)( 30,164)( 31,167)( 32,176)( 33,189)( 34,190)( 35,162)( 36,187)( 37,186)( 38,156)( 39,185)( 40,163)( 41,183)( 42,181)( 43,180)( 44,192)( 45,177)( 46,178)( 47,173)( 48,188)( 49,100)( 50,104)( 51,109)( 52,101)( 53,111)( 54,112)( 55,115)( 56,105)( 57,118)( 58,119)( 59,122)( 60,125)( 61,107)( 62,127)( 63,102)( 64,113)( 65,128)( 66,129)( 67,116)( 68,132)( 69,133)( 70,106)( 71,120)( 72,135)( 73,136)( 74,110)( 75,137)( 76,138)( 77,121)( 78,139)( 79,123)( 80, 97)( 81,130)( 82,140)( 83,141)( 84,117)( 85,134)( 86,143)( 87, 98)( 88,126)( 89, 99)( 90,108)( 91,124)( 92,131)( 93,142)( 94,144)( 95,103)( 96,114);;
s2 := (  1,103)(  2, 99)(  3,113)(  4,115)(  5,116)(  6,117)(  7,114)(  8,109)(  9,107)( 10,110)( 11, 97)( 12,121)( 13,128)( 14,101)( 15,132)( 16,133)( 17,134)( 18,106)( 19,129)( 20,130)( 21,131)( 22,122)( 23,127)( 24,123)( 25,126)( 26,100)( 27,102)( 28,108)( 29,136)( 30,124)( 31,111)( 32,143)( 33,119)( 34,120)( 35, 98)( 36,140)( 37,141)( 38,142)( 39,137)( 40,139)( 41,112)( 42,125)( 43,138)( 44,135)( 45,104)( 46,105)( 47,144)( 48,118)( 49,158)( 50,153)( 51,190)( 52,175)( 53,171)( 54,147)( 55,169)( 56,166)( 57,154)( 58,168)( 59,162)( 60,145)( 61,192)( 62,178)( 63,185)( 64,157)( 65,155)( 66,182)( 67,184)( 68,174)( 69,172)( 70,167)( 71,183)( 72,146)( 73,149)( 74,177)( 75,179)( 76,161)( 77,148)( 78,150)( 79,188)( 80,170)( 81,191)( 82,151)( 83,164)( 84,187)( 85,186)( 86,156)( 87,152)( 88,159)( 89,189)( 90,176)( 91,160)( 92,163)( 93,180)( 94,165)( 95,173)( 96,181);;
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*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(192)!(  2, 30)(  3, 34)(  7, 21)(  8, 43)(  9, 28)( 10, 12)( 11, 35)( 13, 44)( 14, 46)( 18, 27)( 19, 37)( 20, 38)( 22, 42)( 23, 29)( 24, 25)( 26, 45)( 31, 48)( 33, 41)( 36, 47)( 39, 40)( 50, 86)( 51, 62)( 55, 57)( 56, 95)( 58, 68)( 59, 75)( 60, 94)( 61, 79)( 66, 73)( 67, 70)( 69, 72)( 71, 84)( 74, 89)( 76, 83)( 77, 96)( 78, 82)( 81, 88)( 85, 87)( 90, 93)( 91, 92)( 97, 98)( 99,124)(100,104)(101,105)(102,106)(107,108)(109,138)(110,121)(111,118)(112,119)(113,120)(114,131)(122,125)(123,126)(127,136)(128,135)(129,141)(130,142)(137,139)(140,144)(145,165)(146,172)(148,181)(149,182)(150,151)(152,186)(153,156)(154,169)(159,191)(160,163)(161,164)(162,179)(166,173)(167,184)(168,174)(176,180)(177,189)(178,190)(183,187)(188,192);
s1 := Sym(192)!(  1,145)(  2,147)(  3,146)(  4,148)(  5,149)(  6,150)(  7,169)(  8,157)(  9,155)( 10,158)( 11,153)( 12,182)( 13,152)( 14,154)( 15,159)( 16,160)( 17,161)( 18,179)( 19,184)( 20,174)( 21,172)( 22,170)( 23,175)( 24,171)( 25,151)( 26,166)( 27,168)( 28,165)( 29,191)( 30,164)( 31,167)( 32,176)( 33,189)( 34,190)( 35,162)( 36,187)( 37,186)( 38,156)( 39,185)( 40,163)( 41,183)( 42,181)( 43,180)( 44,192)( 45,177)( 46,178)( 47,173)( 48,188)( 49,100)( 50,104)( 51,109)( 52,101)( 53,111)( 54,112)( 55,115)( 56,105)( 57,118)( 58,119)( 59,122)( 60,125)( 61,107)( 62,127)( 63,102)( 64,113)( 65,128)( 66,129)( 67,116)( 68,132)( 69,133)( 70,106)( 71,120)( 72,135)( 73,136)( 74,110)( 75,137)( 76,138)( 77,121)( 78,139)( 79,123)( 80, 97)( 81,130)( 82,140)( 83,141)( 84,117)( 85,134)( 86,143)( 87, 98)( 88,126)( 89, 99)( 90,108)( 91,124)( 92,131)( 93,142)( 94,144)( 95,103)( 96,114);
s2 := Sym(192)!(  1,103)(  2, 99)(  3,113)(  4,115)(  5,116)(  6,117)(  7,114)(  8,109)(  9,107)( 10,110)( 11, 97)( 12,121)( 13,128)( 14,101)( 15,132)( 16,133)( 17,134)( 18,106)( 19,129)( 20,130)( 21,131)( 22,122)( 23,127)( 24,123)( 25,126)( 26,100)( 27,102)( 28,108)( 29,136)( 30,124)( 31,111)( 32,143)( 33,119)( 34,120)( 35, 98)( 36,140)( 37,141)( 38,142)( 39,137)( 40,139)( 41,112)( 42,125)( 43,138)( 44,135)( 45,104)( 46,105)( 47,144)( 48,118)( 49,158)( 50,153)( 51,190)( 52,175)( 53,171)( 54,147)( 55,169)( 56,166)( 57,154)( 58,168)( 59,162)( 60,145)( 61,192)( 62,178)( 63,185)( 64,157)( 65,155)( 66,182)( 67,184)( 68,174)( 69,172)( 70,167)( 71,183)( 72,146)( 73,149)( 74,177)( 75,179)( 76,161)( 77,148)( 78,150)( 79,188)( 80,170)( 81,191)( 82,151)( 83,164)( 84,187)( 85,186)( 86,156)( 87,152)( 88,159)( 89,189)( 90,176)( 91,160)( 92,163)( 93,180)( 94,165)( 95,173)( 96,181);
poly := sub<Sym(192)|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*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 >;

References