Polytope of Type {4,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48}*384a
Also Known As : {4,48|2}. if this polytope has another name.
Group : SmallGroup(384,1684)
Rank : 3
Schlafli Type : {4,48}
Number of vertices, edges, etc : 4, 96, 48
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,48,2} of size 768
Vertex Figure Of :
   {2,4,48} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,24}*192a, {2,48}*192
   3-fold quotients : {4,16}*128a
   4-fold quotients : {4,12}*96a, {2,24}*96
   6-fold quotients : {4,8}*64a, {2,16}*64
   8-fold quotients : {2,12}*48, {4,6}*48a
   12-fold quotients : {4,4}*32, {2,8}*32
   16-fold quotients : {2,6}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,48}*768a, {8,48}*768c, {8,48}*768d, {4,96}*768a, {4,96}*768b
   3-fold covers : {4,144}*1152a, {12,48}*1152a, {12,48}*1152b
   5-fold covers : {4,240}*1920a, {20,48}*1920a
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, 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)
( 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)
(121,169)(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);;
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)(145,181)(146,183)
(147,182)(148,184)(149,186)(150,185)(151,190)(152,192)(153,191)(154,187)
(155,189)(156,188)(157,169)(158,171)(159,170)(160,172)(161,174)(162,173)
(163,178)(164,180)(165,179)(166,175)(167,177)(168,176);;
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)( 13,110)( 14,109)( 15,111)( 16,113)
( 17,112)( 18,114)( 19,119)( 20,118)( 21,120)( 22,116)( 23,115)( 24,117)
( 25,128)( 26,127)( 27,129)( 28,131)( 29,130)( 30,132)( 31,122)( 32,121)
( 33,123)( 34,125)( 35,124)( 36,126)( 37,140)( 38,139)( 39,141)( 40,143)
( 41,142)( 42,144)( 43,134)( 44,133)( 45,135)( 46,137)( 47,136)( 48,138)
( 49,146)( 50,145)( 51,147)( 52,149)( 53,148)( 54,150)( 55,155)( 56,154)
( 57,156)( 58,152)( 59,151)( 60,153)( 61,158)( 62,157)( 63,159)( 64,161)
( 65,160)( 66,162)( 67,167)( 68,166)( 69,168)( 70,164)( 71,163)( 72,165)
( 73,176)( 74,175)( 75,177)( 76,179)( 77,178)( 78,180)( 79,170)( 80,169)
( 81,171)( 82,173)( 83,172)( 84,174)( 85,188)( 86,187)( 87,189)( 88,191)
( 89,190)( 90,192)( 91,182)( 92,181)( 93,183)( 94,185)( 95,184)( 96,186);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
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