Polytope of Type {48,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1088573)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 96, 192, 8
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,4}*384c
   4-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b
   8-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {8,2}*32
   32-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {4,2}*16
   64-fold quotients : {3,2}*12
   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 := (  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)(  8,152)
(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)( 16,168)
( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)( 24,160)
( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)( 32,188)
( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)( 40,180)
( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)( 48,172)
( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)( 56,104)
( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)( 64,120)
( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)( 72,112)
( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)( 80,140)
( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)( 88,132)
( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)( 96,124);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)(104,115)
(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)(124,135)
(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)(132,143)
(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)(152,163)
(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)(172,183)
(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)(180,191);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*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(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)!(  1,153)(  2,155)(  3,154)(  4,156)(  5,149)(  6,151)(  7,150)
(  8,152)(  9,145)( 10,147)( 11,146)( 12,148)( 13,165)( 14,167)( 15,166)
( 16,168)( 17,161)( 18,163)( 19,162)( 20,164)( 21,157)( 22,159)( 23,158)
( 24,160)( 25,189)( 26,191)( 27,190)( 28,192)( 29,185)( 30,187)( 31,186)
( 32,188)( 33,181)( 34,183)( 35,182)( 36,184)( 37,177)( 38,179)( 39,178)
( 40,180)( 41,173)( 42,175)( 43,174)( 44,176)( 45,169)( 46,171)( 47,170)
( 48,172)( 49,105)( 50,107)( 51,106)( 52,108)( 53,101)( 54,103)( 55,102)
( 56,104)( 57, 97)( 58, 99)( 59, 98)( 60,100)( 61,117)( 62,119)( 63,118)
( 64,120)( 65,113)( 66,115)( 67,114)( 68,116)( 69,109)( 70,111)( 71,110)
( 72,112)( 73,141)( 74,143)( 75,142)( 76,144)( 77,137)( 78,139)( 79,138)
( 80,140)( 81,133)( 82,135)( 83,134)( 84,136)( 85,129)( 86,131)( 87,130)
( 88,132)( 89,125)( 90,127)( 91,126)( 92,128)( 93,121)( 94,123)( 95,122)
( 96,124);
s2 := Sym(192)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97,110)( 98,109)( 99,112)(100,111)(101,114)(102,113)(103,116)
(104,115)(105,118)(106,117)(107,120)(108,119)(121,134)(122,133)(123,136)
(124,135)(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)
(132,143)(145,158)(146,157)(147,160)(148,159)(149,162)(150,161)(151,164)
(152,163)(153,166)(154,165)(155,168)(156,167)(169,182)(170,181)(171,184)
(172,183)(173,186)(174,185)(175,188)(176,187)(177,190)(178,189)(179,192)
(180,191);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*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 : None.
to this polytope