Polytope of Type {2,4,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,48}*768b
if this polytope has a name.
Group : SmallGroup(768,323454)
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
   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}*384a
   3-fold quotients : {2,4,16}*256b
   4-fold quotients : {2,4,12}*192a, {2,2,24}*192
   6-fold quotients : {2,4,8}*128a
   8-fold quotients : {2,2,12}*96, {2,4,6}*96a
   12-fold quotients : {2,4,4}*64, {2,2,8}*64
   16-fold quotients : {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope