Polytope of Type {6,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*768b
if this polytope has a name.
Group : SmallGroup(768,1088591)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 8, 192, 64
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,24}*384a
   4-fold quotients : {6,12}*192a
   8-fold quotients : {6,6}*96
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {2,8}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {2,4}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope