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Polytope of Type {2,4,22,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,22,4}*1408
if this polytope has a name.
Group : SmallGroup(1408,17946)
Rank : 5
Schlafli Type : {2,4,22,4}
Number of vertices, edges, etc : 2, 4, 44, 44, 4
Order of s0s1s2s3s4 : 44
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,22,4}*704, {2,4,22,2}*704
   4-fold quotients : {2,2,22,2}*352
   8-fold quotients : {2,2,11,2}*176
   11-fold quotients : {2,4,2,4}*128
   22-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
   44-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 91,113)( 92,114)( 93,115)( 94,116)( 95,117)( 96,118)( 97,119)( 98,120)
( 99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)(106,128)
(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(135,157)(136,158)
(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)(144,166)
(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)(152,174)
(153,175)(154,176)(155,177)(156,178);;
s2 := (  3, 91)(  4,101)(  5,100)(  6, 99)(  7, 98)(  8, 97)(  9, 96)( 10, 95)
( 11, 94)( 12, 93)( 13, 92)( 14,102)( 15,112)( 16,111)( 17,110)( 18,109)
( 19,108)( 20,107)( 21,106)( 22,105)( 23,104)( 24,103)( 25,113)( 26,123)
( 27,122)( 28,121)( 29,120)( 30,119)( 31,118)( 32,117)( 33,116)( 34,115)
( 35,114)( 36,124)( 37,134)( 38,133)( 39,132)( 40,131)( 41,130)( 42,129)
( 43,128)( 44,127)( 45,126)( 46,125)( 47,157)( 48,167)( 49,166)( 50,165)
( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)( 58,168)
( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,171)
( 67,170)( 68,169)( 69,135)( 70,145)( 71,144)( 72,143)( 73,142)( 74,141)
( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,146)( 81,156)( 82,155)
( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)( 88,149)( 89,148)( 90,147);;
s3 := (  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)( 17, 23)
( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)( 36, 37)
( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 81)( 48, 80)( 49, 90)( 50, 89)
( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 70)
( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)
( 67, 72)( 68, 71)( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)(102,103)
(104,112)(105,111)(106,110)(107,109)(113,114)(115,123)(116,122)(117,121)
(118,120)(124,125)(126,134)(127,133)(128,132)(129,131)(135,169)(136,168)
(137,178)(138,177)(139,176)(140,175)(141,174)(142,173)(143,172)(144,171)
(145,170)(146,158)(147,157)(148,167)(149,166)(150,165)(151,164)(152,163)
(153,162)(154,161)(155,160)(156,159);;
s4 := (  3, 47)(  4, 48)(  5, 49)(  6, 50)(  7, 51)(  8, 52)(  9, 53)( 10, 54)
( 11, 55)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 62)
( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25, 69)( 26, 70)
( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)( 34, 78)
( 35, 79)( 36, 80)( 37, 81)( 38, 82)( 39, 83)( 40, 84)( 41, 85)( 42, 86)
( 43, 87)( 44, 88)( 45, 89)( 46, 90)( 91,157)( 92,158)( 93,159)( 94,160)
( 95,161)( 96,162)( 97,163)( 98,164)( 99,165)(100,166)(101,167)(102,168)
(103,169)(104,170)(105,171)(106,172)(107,173)(108,174)(109,175)(110,176)
(111,177)(112,178)(113,135)(114,136)(115,137)(116,138)(117,139)(118,140)
(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)(126,148)
(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)(134,156);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(178)!(1,2);
s1 := Sym(178)!( 91,113)( 92,114)( 93,115)( 94,116)( 95,117)( 96,118)( 97,119)
( 98,120)( 99,121)(100,122)(101,123)(102,124)(103,125)(104,126)(105,127)
(106,128)(107,129)(108,130)(109,131)(110,132)(111,133)(112,134)(135,157)
(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)(142,164)(143,165)
(144,166)(145,167)(146,168)(147,169)(148,170)(149,171)(150,172)(151,173)
(152,174)(153,175)(154,176)(155,177)(156,178);
s2 := Sym(178)!(  3, 91)(  4,101)(  5,100)(  6, 99)(  7, 98)(  8, 97)(  9, 96)
( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14,102)( 15,112)( 16,111)( 17,110)
( 18,109)( 19,108)( 20,107)( 21,106)( 22,105)( 23,104)( 24,103)( 25,113)
( 26,123)( 27,122)( 28,121)( 29,120)( 30,119)( 31,118)( 32,117)( 33,116)
( 34,115)( 35,114)( 36,124)( 37,134)( 38,133)( 39,132)( 40,131)( 41,130)
( 42,129)( 43,128)( 44,127)( 45,126)( 46,125)( 47,157)( 48,167)( 49,166)
( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,158)
( 58,168)( 59,178)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)
( 66,171)( 67,170)( 68,169)( 69,135)( 70,145)( 71,144)( 72,143)( 73,142)
( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,146)( 81,156)
( 82,155)( 83,154)( 84,153)( 85,152)( 86,151)( 87,150)( 88,149)( 89,148)
( 90,147);
s3 := Sym(178)!(  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 25, 26)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 36, 37)( 38, 46)( 39, 45)( 40, 44)( 41, 43)( 47, 81)( 48, 80)( 49, 90)
( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 70)( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 91, 92)( 93,101)( 94,100)( 95, 99)( 96, 98)
(102,103)(104,112)(105,111)(106,110)(107,109)(113,114)(115,123)(116,122)
(117,121)(118,120)(124,125)(126,134)(127,133)(128,132)(129,131)(135,169)
(136,168)(137,178)(138,177)(139,176)(140,175)(141,174)(142,173)(143,172)
(144,171)(145,170)(146,158)(147,157)(148,167)(149,166)(150,165)(151,164)
(152,163)(153,162)(154,161)(155,160)(156,159);
s4 := Sym(178)!(  3, 47)(  4, 48)(  5, 49)(  6, 50)(  7, 51)(  8, 52)(  9, 53)
( 10, 54)( 11, 55)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 61)
( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23, 67)( 24, 68)( 25, 69)
( 26, 70)( 27, 71)( 28, 72)( 29, 73)( 30, 74)( 31, 75)( 32, 76)( 33, 77)
( 34, 78)( 35, 79)( 36, 80)( 37, 81)( 38, 82)( 39, 83)( 40, 84)( 41, 85)
( 42, 86)( 43, 87)( 44, 88)( 45, 89)( 46, 90)( 91,157)( 92,158)( 93,159)
( 94,160)( 95,161)( 96,162)( 97,163)( 98,164)( 99,165)(100,166)(101,167)
(102,168)(103,169)(104,170)(105,171)(106,172)(107,173)(108,174)(109,175)
(110,176)(111,177)(112,178)(113,135)(114,136)(115,137)(116,138)(117,139)
(118,140)(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)
(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)
(134,156);
poly := sub<Sym(178)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, 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 >; 
 

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