Polytope of Type {2,48,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1088569)
Rank : 4
Schlafli Type : {2,48,4}
Number of vertices, edges, etc : 2, 48, 96, 4
Order of s₀s₁s₂s₃ : 48
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
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 : {2,24,4}*384c
   4-fold quotients : {2,12,4}*192b
   8-fold quotients : {2,6,4}*96c
   16-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)
( 21, 24)( 22, 26)( 27, 39)( 28, 41)( 29, 40)( 30, 42)( 31, 47)( 32, 49)
( 33, 48)( 34, 50)( 35, 43)( 36, 45)( 37, 44)( 38, 46)( 51, 75)( 52, 77)
( 53, 76)( 54, 78)( 55, 83)( 56, 85)( 57, 84)( 58, 86)( 59, 79)( 60, 81)
( 61, 80)( 62, 82)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 95)( 68, 97)
( 69, 96)( 70, 98)( 71, 91)( 72, 93)( 73, 92)( 74, 94)( 99,147)(100,149)
(101,148)(102,150)(103,155)(104,157)(105,156)(106,158)(107,151)(108,153)
(109,152)(110,154)(111,159)(112,161)(113,160)(114,162)(115,167)(116,169)
(117,168)(118,170)(119,163)(120,165)(121,164)(122,166)(123,183)(124,185)
(125,184)(126,186)(127,191)(128,193)(129,192)(130,194)(131,187)(132,189)
(133,188)(134,190)(135,171)(136,173)(137,172)(138,174)(139,179)(140,181)
(141,180)(142,182)(143,175)(144,177)(145,176)(146,178);;
s2 := (  3,103)(  4,104)(  5,106)(  6,105)(  7, 99)(  8,100)(  9,102)( 10,101)
( 11,107)( 12,108)( 13,110)( 14,109)( 15,115)( 16,116)( 17,118)( 18,117)
( 19,111)( 20,112)( 21,114)( 22,113)( 23,119)( 24,120)( 25,122)( 26,121)
( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)( 34,137)
( 35,143)( 36,144)( 37,146)( 38,145)( 39,127)( 40,128)( 41,130)( 42,129)
( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)( 50,133)
( 51,175)( 52,176)( 53,178)( 54,177)( 55,171)( 56,172)( 57,174)( 58,173)
( 59,179)( 60,180)( 61,182)( 62,181)( 63,187)( 64,188)( 65,190)( 66,189)
( 67,183)( 68,184)( 69,186)( 70,185)( 71,191)( 72,192)( 73,194)( 74,193)
( 75,151)( 76,152)( 77,154)( 78,153)( 79,147)( 80,148)( 81,150)( 82,149)
( 83,155)( 84,156)( 85,158)( 86,157)( 87,163)( 88,164)( 89,166)( 90,165)
( 91,159)( 92,160)( 93,162)( 94,161)( 95,167)( 96,168)( 97,170)( 98,169);;
s3 := (  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 22)(  8, 21)(  9, 20)( 10, 19)
( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 27, 42)( 28, 41)( 29, 40)( 30, 39)
( 31, 46)( 32, 45)( 33, 44)( 34, 43)( 35, 50)( 36, 49)( 37, 48)( 38, 47)
( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 70)( 56, 69)( 57, 68)( 58, 67)
( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 75, 90)( 76, 89)( 77, 88)( 78, 87)
( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 98)( 84, 97)( 85, 96)( 86, 95)
( 99,114)(100,113)(101,112)(102,111)(103,118)(104,117)(105,116)(106,115)
(107,122)(108,121)(109,120)(110,119)(123,138)(124,137)(125,136)(126,135)
(127,142)(128,141)(129,140)(130,139)(131,146)(132,145)(133,144)(134,143)
(147,162)(148,161)(149,160)(150,159)(151,166)(152,165)(153,164)(154,163)
(155,170)(156,169)(157,168)(158,167)(171,186)(172,185)(173,184)(174,183)
(175,190)(176,189)(177,188)(178,187)(179,194)(180,193)(181,192)(182,191);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(194)!(1,2);
s1 := Sym(194)!(  4,  5)(  7, 11)(  8, 13)(  9, 12)( 10, 14)( 16, 17)( 19, 23)
( 20, 25)( 21, 24)( 22, 26)( 27, 39)( 28, 41)( 29, 40)( 30, 42)( 31, 47)
( 32, 49)( 33, 48)( 34, 50)( 35, 43)( 36, 45)( 37, 44)( 38, 46)( 51, 75)
( 52, 77)( 53, 76)( 54, 78)( 55, 83)( 56, 85)( 57, 84)( 58, 86)( 59, 79)
( 60, 81)( 61, 80)( 62, 82)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 95)
( 68, 97)( 69, 96)( 70, 98)( 71, 91)( 72, 93)( 73, 92)( 74, 94)( 99,147)
(100,149)(101,148)(102,150)(103,155)(104,157)(105,156)(106,158)(107,151)
(108,153)(109,152)(110,154)(111,159)(112,161)(113,160)(114,162)(115,167)
(116,169)(117,168)(118,170)(119,163)(120,165)(121,164)(122,166)(123,183)
(124,185)(125,184)(126,186)(127,191)(128,193)(129,192)(130,194)(131,187)
(132,189)(133,188)(134,190)(135,171)(136,173)(137,172)(138,174)(139,179)
(140,181)(141,180)(142,182)(143,175)(144,177)(145,176)(146,178);
s2 := Sym(194)!(  3,103)(  4,104)(  5,106)(  6,105)(  7, 99)(  8,100)(  9,102)
( 10,101)( 11,107)( 12,108)( 13,110)( 14,109)( 15,115)( 16,116)( 17,118)
( 18,117)( 19,111)( 20,112)( 21,114)( 22,113)( 23,119)( 24,120)( 25,122)
( 26,121)( 27,139)( 28,140)( 29,142)( 30,141)( 31,135)( 32,136)( 33,138)
( 34,137)( 35,143)( 36,144)( 37,146)( 38,145)( 39,127)( 40,128)( 41,130)
( 42,129)( 43,123)( 44,124)( 45,126)( 46,125)( 47,131)( 48,132)( 49,134)
( 50,133)( 51,175)( 52,176)( 53,178)( 54,177)( 55,171)( 56,172)( 57,174)
( 58,173)( 59,179)( 60,180)( 61,182)( 62,181)( 63,187)( 64,188)( 65,190)
( 66,189)( 67,183)( 68,184)( 69,186)( 70,185)( 71,191)( 72,192)( 73,194)
( 74,193)( 75,151)( 76,152)( 77,154)( 78,153)( 79,147)( 80,148)( 81,150)
( 82,149)( 83,155)( 84,156)( 85,158)( 86,157)( 87,163)( 88,164)( 89,166)
( 90,165)( 91,159)( 92,160)( 93,162)( 94,161)( 95,167)( 96,168)( 97,170)
( 98,169);
s3 := Sym(194)!(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 22)(  8, 21)(  9, 20)
( 10, 19)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 27, 42)( 28, 41)( 29, 40)
( 30, 39)( 31, 46)( 32, 45)( 33, 44)( 34, 43)( 35, 50)( 36, 49)( 37, 48)
( 38, 47)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 70)( 56, 69)( 57, 68)
( 58, 67)( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 75, 90)( 76, 89)( 77, 88)
( 78, 87)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 98)( 84, 97)( 85, 96)
( 86, 95)( 99,114)(100,113)(101,112)(102,111)(103,118)(104,117)(105,116)
(106,115)(107,122)(108,121)(109,120)(110,119)(123,138)(124,137)(125,136)
(126,135)(127,142)(128,141)(129,140)(130,139)(131,146)(132,145)(133,144)
(134,143)(147,162)(148,161)(149,160)(150,159)(151,166)(152,165)(153,164)
(154,163)(155,170)(156,169)(157,168)(158,167)(171,186)(172,185)(173,184)
(174,183)(175,190)(176,189)(177,188)(178,187)(179,194)(180,193)(181,192)
(182,191);
poly := sub<Sym(194)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s1*s2 >;

to this polytope