Polytope of Type {48,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4}*384b
if this polytope has a name.
Group : SmallGroup(384,1696)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 48, 96, 4
Order of s₀s₁s₂ : 48
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {48,4,2} of size 768
Vertex Figure Of :
   {2,48,4} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,4}*192a
   3-fold quotients : {16,4}*128b
   4-fold quotients : {12,4}*96a, {24,2}*96
   6-fold quotients : {8,4}*64a
   8-fold quotients : {12,2}*48, {6,4}*48a
   12-fold quotients : {4,4}*32, {8,2}*32
   16-fold quotients : {6,2}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {3,2}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,4}*768a, {48,8}*768e, {48,8}*768f
   3-fold covers : {144,4}*1152b, {48,12}*1152d, {48,12}*1152e
   5-fold covers : {240,4}*1920b, {48,20}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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