Polytope of Type {48,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*768a
if this polytope has a name.
Group : SmallGroup(768,1088585)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 64, 192, 8
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,6}*384a
   4-fold quotients : {12,6}*192a
   8-fold quotients : {6,6}*96
   12-fold quotients : {16,2}*64
   16-fold quotients : {3,6}*48, {6,3}*48
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,3}*24
   48-fold quotients : {4,2}*16
   96-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope