Polytope of Type {2,4,48}

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

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

Permutation Representation (Magma) :

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

to this polytope