Polytope of Type {6,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*768a
if this polytope has a name.
Group : SmallGroup(768,1088585)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 8, 192, 64
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 6
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
   12-fold quotients : {2,16}*64
   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,  9)(  6, 10)(  7, 12)(  8, 11)( 15, 16)( 17, 21)( 18, 22)
( 19, 24)( 20, 23)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 39, 40)
( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)( 55, 60)
( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 81)
( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)( 92, 95)
( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)(114,118)
(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)(135,136)
(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)(151,156)
(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)(173,177)
(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)(188,191);;
s1 := (  1,  9)(  2, 11)(  3, 10)(  4, 12)(  6,  7)( 13, 21)( 14, 23)( 15, 22)
( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)( 30, 43)
( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 81)( 50, 83)
( 51, 82)( 52, 84)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 73)( 58, 75)
( 59, 74)( 60, 76)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 65, 89)( 66, 91)
( 67, 90)( 68, 92)( 69, 85)( 70, 87)( 71, 86)( 72, 88)( 97,153)( 98,155)
( 99,154)(100,156)(101,149)(102,151)(103,150)(104,152)(105,145)(106,147)
(107,146)(108,148)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)
(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,189)(122,191)
(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)(129,181)(130,183)
(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)(137,173)(138,175)
(139,174)(140,176)(141,169)(142,171)(143,170)(144,172);;
s2 := (  1, 98)(  2, 97)(  3, 99)(  4,100)(  5,106)(  6,105)(  7,107)(  8,108)
(  9,102)( 10,101)( 11,103)( 12,104)( 13,110)( 14,109)( 15,111)( 16,112)
( 17,118)( 18,117)( 19,119)( 20,120)( 21,114)( 22,113)( 23,115)( 24,116)
( 25,134)( 26,133)( 27,135)( 28,136)( 29,142)( 30,141)( 31,143)( 32,144)
( 33,138)( 34,137)( 35,139)( 36,140)( 37,122)( 38,121)( 39,123)( 40,124)
( 41,130)( 42,129)( 43,131)( 44,132)( 45,126)( 46,125)( 47,127)( 48,128)
( 49,170)( 50,169)( 51,171)( 52,172)( 53,178)( 54,177)( 55,179)( 56,180)
( 57,174)( 58,173)( 59,175)( 60,176)( 61,182)( 62,181)( 63,183)( 64,184)
( 65,190)( 66,189)( 67,191)( 68,192)( 69,186)( 70,185)( 71,187)( 72,188)
( 73,146)( 74,145)( 75,147)( 76,148)( 77,154)( 78,153)( 79,155)( 80,156)
( 81,150)( 82,149)( 83,151)( 84,152)( 85,158)( 86,157)( 87,159)( 88,160)
( 89,166)( 90,165)( 91,167)( 92,168)( 93,162)( 94,161)( 95,163)( 96,164);;
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*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 ];;
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)( 27, 28)( 29, 33)( 30, 34)( 31, 36)( 32, 35)
( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 51, 52)( 53, 57)( 54, 58)
( 55, 60)( 56, 59)( 63, 64)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)
( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 87, 88)( 89, 93)( 90, 94)( 91, 96)
( 92, 95)( 99,100)(101,105)(102,106)(103,108)(104,107)(111,112)(113,117)
(114,118)(115,120)(116,119)(123,124)(125,129)(126,130)(127,132)(128,131)
(135,136)(137,141)(138,142)(139,144)(140,143)(147,148)(149,153)(150,154)
(151,156)(152,155)(159,160)(161,165)(162,166)(163,168)(164,167)(171,172)
(173,177)(174,178)(175,180)(176,179)(183,184)(185,189)(186,190)(187,192)
(188,191);
s1 := Sym(192)!(  1,  9)(  2, 11)(  3, 10)(  4, 12)(  6,  7)( 13, 21)( 14, 23)
( 15, 22)( 16, 24)( 18, 19)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 41)
( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)( 36, 40)( 49, 81)
( 50, 83)( 51, 82)( 52, 84)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 73)
( 58, 75)( 59, 74)( 60, 76)( 61, 93)( 62, 95)( 63, 94)( 64, 96)( 65, 89)
( 66, 91)( 67, 90)( 68, 92)( 69, 85)( 70, 87)( 71, 86)( 72, 88)( 97,153)
( 98,155)( 99,154)(100,156)(101,149)(102,151)(103,150)(104,152)(105,145)
(106,147)(107,146)(108,148)(109,165)(110,167)(111,166)(112,168)(113,161)
(114,163)(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,189)
(122,191)(123,190)(124,192)(125,185)(126,187)(127,186)(128,188)(129,181)
(130,183)(131,182)(132,184)(133,177)(134,179)(135,178)(136,180)(137,173)
(138,175)(139,174)(140,176)(141,169)(142,171)(143,170)(144,172);
s2 := Sym(192)!(  1, 98)(  2, 97)(  3, 99)(  4,100)(  5,106)(  6,105)(  7,107)
(  8,108)(  9,102)( 10,101)( 11,103)( 12,104)( 13,110)( 14,109)( 15,111)
( 16,112)( 17,118)( 18,117)( 19,119)( 20,120)( 21,114)( 22,113)( 23,115)
( 24,116)( 25,134)( 26,133)( 27,135)( 28,136)( 29,142)( 30,141)( 31,143)
( 32,144)( 33,138)( 34,137)( 35,139)( 36,140)( 37,122)( 38,121)( 39,123)
( 40,124)( 41,130)( 42,129)( 43,131)( 44,132)( 45,126)( 46,125)( 47,127)
( 48,128)( 49,170)( 50,169)( 51,171)( 52,172)( 53,178)( 54,177)( 55,179)
( 56,180)( 57,174)( 58,173)( 59,175)( 60,176)( 61,182)( 62,181)( 63,183)
( 64,184)( 65,190)( 66,189)( 67,191)( 68,192)( 69,186)( 70,185)( 71,187)
( 72,188)( 73,146)( 74,145)( 75,147)( 76,148)( 77,154)( 78,153)( 79,155)
( 80,156)( 81,150)( 82,149)( 83,151)( 84,152)( 85,158)( 86,157)( 87,159)
( 88,160)( 89,166)( 90,165)( 91,167)( 92,168)( 93,162)( 94,161)( 95,163)
( 96,164);
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*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2 >;

References : None.
to this polytope