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Polytope of Type {2,88,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,88,4}*1408b
if this polytope has a name.
Group : SmallGroup(1408,13836)
Rank : 4
Schlafli Type : {2,88,4}
Number of vertices, edges, etc : 2, 88, 176, 4
Order of s0s1s2s3 : 88
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 : {2,44,4}*704
   4-fold quotients : {2,44,2}*352, {2,22,4}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {2,8,4}*128b
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {2,4,4}*64
   44-fold quotients : {2,2,4}*32, {2,4,2}*32
   88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)( 30, 42)
( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 58)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)( 96,141)
( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)(104,155)
(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)
(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)
(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)(128,164)
(129,163)(130,162)(131,161)(132,160)(133,159)(134,158);;
s2 := (  3, 92)(  4, 91)(  5,101)(  6,100)(  7, 99)(  8, 98)(  9, 97)( 10, 96)
( 11, 95)( 12, 94)( 13, 93)( 14,103)( 15,102)( 16,112)( 17,111)( 18,110)
( 19,109)( 20,108)( 21,107)( 22,106)( 23,105)( 24,104)( 25,114)( 26,113)
( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)( 34,116)
( 35,115)( 36,125)( 37,124)( 38,134)( 39,133)( 40,132)( 41,131)( 42,130)
( 43,129)( 44,128)( 45,127)( 46,126)( 47,147)( 48,146)( 49,156)( 50,155)
( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)( 58,136)
( 59,135)( 60,145)( 61,144)( 62,143)( 63,142)( 64,141)( 65,140)( 66,139)
( 67,138)( 68,137)( 69,169)( 70,168)( 71,178)( 72,177)( 73,176)( 74,175)
( 75,174)( 76,173)( 77,172)( 78,171)( 79,170)( 80,158)( 81,157)( 82,167)
( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)( 88,161)( 89,160)( 90,159);;
s3 := ( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)( 54, 65)
( 55, 66)( 56, 67)( 57, 68)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)
( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 78, 89)( 79, 90)( 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)(135,168)(136,169)(137,170)(138,171)
(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)(146,157)
(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)(154,165)
(155,166)(156,167);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s3*s2*s1*s2*s1*s3*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(178)!(1,2);
s1 := Sym(178)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 25, 36)( 26, 46)( 27, 45)( 28, 44)( 29, 43)
( 30, 42)( 31, 41)( 32, 40)( 33, 39)( 34, 38)( 35, 37)( 47, 58)( 48, 68)
( 49, 67)( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)
( 57, 59)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 91,135)( 92,145)( 93,144)( 94,143)( 95,142)
( 96,141)( 97,140)( 98,139)( 99,138)(100,137)(101,136)(102,146)(103,156)
(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)
(112,147)(113,168)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)
(120,172)(121,171)(122,170)(123,169)(124,157)(125,167)(126,166)(127,165)
(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158);
s2 := Sym(178)!(  3, 92)(  4, 91)(  5,101)(  6,100)(  7, 99)(  8, 98)(  9, 97)
( 10, 96)( 11, 95)( 12, 94)( 13, 93)( 14,103)( 15,102)( 16,112)( 17,111)
( 18,110)( 19,109)( 20,108)( 21,107)( 22,106)( 23,105)( 24,104)( 25,114)
( 26,113)( 27,123)( 28,122)( 29,121)( 30,120)( 31,119)( 32,118)( 33,117)
( 34,116)( 35,115)( 36,125)( 37,124)( 38,134)( 39,133)( 40,132)( 41,131)
( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,147)( 48,146)( 49,156)
( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)
( 58,136)( 59,135)( 60,145)( 61,144)( 62,143)( 63,142)( 64,141)( 65,140)
( 66,139)( 67,138)( 68,137)( 69,169)( 70,168)( 71,178)( 72,177)( 73,176)
( 74,175)( 75,174)( 76,173)( 77,172)( 78,171)( 79,170)( 80,158)( 81,157)
( 82,167)( 83,166)( 84,165)( 85,164)( 86,163)( 87,162)( 88,161)( 89,160)
( 90,159);
s3 := Sym(178)!( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)( 53, 64)
( 54, 65)( 55, 66)( 56, 67)( 57, 68)( 69, 80)( 70, 81)( 71, 82)( 72, 83)
( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 78, 89)( 79, 90)( 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)(135,168)(136,169)(137,170)
(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,177)(145,178)
(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)(153,164)
(154,165)(155,166)(156,167);
poly := sub<Sym(178)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s3*s2*s1*s2*s1*s3*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 >; 
 

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