Polytope of Type {4,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48}*384d
if this polytope has a name.
Group : SmallGroup(384,5611)
Rank : 3
Schlafli Type : {4,48}
Number of vertices, edges, etc : 4, 96, 48
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,48,2} of size 768
Vertex Figure Of :
   {2,4,48} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,24}*192c
   4-fold quotients : {4,12}*96b
   8-fold quotients : {4,6}*48c
   16-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,48}*768c
   3-fold covers : {4,144}*1152d
   5-fold covers : {4,240}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope