Polytope of Type {4,48,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48,2}*768b
if this polytope has a name.
Group : SmallGroup(768,323454)
Rank : 4
Schlafli Type : {4,48,2}
Number of vertices, edges, etc : 4, 96, 48, 2
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 : {4,24,2}*384a
   3-fold quotients : {4,16,2}*256b
   4-fold quotients : {4,12,2}*192a, {2,24,2}*192
   6-fold quotients : {4,8,2}*128a
   8-fold quotients : {2,12,2}*96, {4,6,2}*96a
   12-fold quotients : {4,4,2}*64, {2,8,2}*64
   16-fold quotients : {2,6,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*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, 49)(  2, 50)(  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, 76)( 26, 77)( 27, 78)( 28, 73)( 29, 74)( 30, 75)( 31, 82)( 32, 83)( 33, 84)( 34, 79)( 35, 80)( 36, 81)( 37, 88)( 38, 89)( 39, 90)( 40, 85)( 41, 86)( 42, 87)( 43, 94)( 44, 95)( 45, 96)( 46, 91)( 47, 92)( 48, 93)( 97,145)( 98,146)( 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)(121,172)(122,173)(123,174)(124,169)(125,170)(126,171)(127,178)(128,179)(129,180)(130,175)(131,176)(132,177)(133,184)(134,185)(135,186)(136,181)(137,182)(138,183)(139,190)(140,191)(141,192)(142,187)(143,188)(144,189);;
s1 := (  2,  3)(  5,  6)(  7, 10)(  8, 12)(  9, 11)( 14, 15)( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 31)( 26, 33)( 27, 32)( 28, 34)( 29, 36)( 30, 35)( 37, 43)( 38, 45)( 39, 44)( 40, 46)( 41, 48)( 42, 47)( 49, 61)( 50, 63)( 51, 62)( 52, 64)( 53, 66)( 54, 65)( 55, 70)( 56, 72)( 57, 71)( 58, 67)( 59, 69)( 60, 68)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 85)( 80, 87)( 81, 86)( 82, 88)( 83, 90)( 84, 89)( 97,121)( 98,123)( 99,122)(100,124)(101,126)(102,125)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)(109,133)(110,135)(111,134)(112,136)(113,138)(114,137)(115,142)(116,144)(117,143)(118,139)(119,141)(120,140)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,190)(155,192)(156,191)(157,172)(158,174)(159,173)(160,169)(161,171)(162,170)(163,175)(164,177)(165,176)(166,178)(167,180)(168,179);;
s2 := (  1, 98)(  2, 97)(  3, 99)(  4,101)(  5,100)(  6,102)(  7,107)(  8,106)(  9,108)( 10,104)( 11,103)( 12,105)( 13,113)( 14,112)( 15,114)( 16,110)( 17,109)( 18,111)( 19,116)( 20,115)( 21,117)( 22,119)( 23,118)( 24,120)( 25,128)( 26,127)( 27,129)( 28,131)( 29,130)( 30,132)( 31,122)( 32,121)( 33,123)( 34,125)( 35,124)( 36,126)( 37,143)( 38,142)( 39,144)( 40,140)( 41,139)( 42,141)( 43,137)( 44,136)( 45,138)( 46,134)( 47,133)( 48,135)( 49,146)( 50,145)( 51,147)( 52,149)( 53,148)( 54,150)( 55,155)( 56,154)( 57,156)( 58,152)( 59,151)( 60,153)( 61,161)( 62,160)( 63,162)( 64,158)( 65,157)( 66,159)( 67,164)( 68,163)( 69,165)( 70,167)( 71,166)( 72,168)( 73,176)( 74,175)( 75,177)( 76,179)( 77,178)( 78,180)( 79,170)( 80,169)( 81,171)( 82,173)( 83,172)( 84,174)( 85,191)( 86,190)( 87,192)( 88,188)( 89,187)( 90,189)( 91,185)( 92,184)( 93,186)( 94,182)( 95,181)( 96,183);;
s3 := (193,194);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
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*s0*s1*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope