Polytope of Type {48,4}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope