Polytope of Type {2,48,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,48,4}*768a
if this polytope has a name.
Group : SmallGroup(768,323306)
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
   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}*384a, {2,48,2}*384
   3-fold quotients : {2,16,4}*256a
   4-fold quotients : {2,12,4}*192a, {2,24,2}*192
   6-fold quotients : {2,8,4}*128a, {2,16,2}*128
   8-fold quotients : {2,12,2}*96, {2,6,4}*96a
   12-fold quotients : {2,4,4}*64, {2,8,2}*64
   16-fold quotients : {2,6,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,3,2}*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, 99)(  4,101)(  5,100)(  6,102)(  7,104)(  8,103)(  9,108)( 10,110)
( 11,109)( 12,105)( 13,107)( 14,106)( 15,111)( 16,113)( 17,112)( 18,114)
( 19,116)( 20,115)( 21,120)( 22,122)( 23,121)( 24,117)( 25,119)( 26,118)
( 27,129)( 28,131)( 29,130)( 30,132)( 31,134)( 32,133)( 33,123)( 34,125)
( 35,124)( 36,126)( 37,128)( 38,127)( 39,141)( 40,143)( 41,142)( 42,144)
( 43,146)( 44,145)( 45,135)( 46,137)( 47,136)( 48,138)( 49,140)( 50,139)
( 51,147)( 52,149)( 53,148)( 54,150)( 55,152)( 56,151)( 57,156)( 58,158)
( 59,157)( 60,153)( 61,155)( 62,154)( 63,159)( 64,161)( 65,160)( 66,162)
( 67,164)( 68,163)( 69,168)( 70,170)( 71,169)( 72,165)( 73,167)( 74,166)
( 75,177)( 76,179)( 77,178)( 78,180)( 79,182)( 80,181)( 81,171)( 82,173)
( 83,172)( 84,174)( 85,176)( 86,175)( 87,189)( 88,191)( 89,190)( 90,192)
( 91,194)( 92,193)( 93,183)( 94,185)( 95,184)( 96,186)( 97,188)( 98,187);;
s2 := (  3,  4)(  6,  7)(  9, 13)( 10, 12)( 11, 14)( 15, 16)( 18, 19)( 21, 25)
( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)
( 39, 46)( 40, 45)( 41, 47)( 42, 49)( 43, 48)( 44, 50)( 51, 64)( 52, 63)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 73)( 58, 72)( 59, 74)( 60, 70)
( 61, 69)( 62, 71)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)
( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)
(101,125)(102,127)(103,126)(104,128)(105,133)(106,132)(107,134)(108,130)
(109,129)(110,131)(111,136)(112,135)(113,137)(114,139)(115,138)(116,140)
(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,184)(148,183)
(149,185)(150,187)(151,186)(152,188)(153,193)(154,192)(155,194)(156,190)
(157,189)(158,191)(159,172)(160,171)(161,173)(162,175)(163,174)(164,176)
(165,181)(166,180)(167,182)(168,178)(169,177)(170,179);;
s3 := (  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, 75)( 28, 76)( 29, 77)( 30, 78)( 31, 79)( 32, 80)( 33, 81)( 34, 82)
( 35, 83)( 36, 84)( 37, 85)( 38, 86)( 39, 87)( 40, 88)( 41, 89)( 42, 90)
( 43, 91)( 44, 92)( 45, 93)( 46, 94)( 47, 95)( 48, 96)( 49, 97)( 50, 98)
( 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)
(123,171)(124,172)(125,173)(126,174)(127,175)(128,176)(129,177)(130,178)
(131,179)(132,180)(133,181)(134,182)(135,183)(136,184)(137,185)(138,186)
(139,187)(140,188)(141,189)(142,190)(143,191)(144,192)(145,193)(146,194);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope