Polytope of Type {4,88,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,88,2}*1408a
if this polytope has a name.
Group : SmallGroup(1408,13688)
Rank : 4
Schlafli Type : {4,88,2}
Number of vertices, edges, etc : 4, 176, 88, 2
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 : {4,44,2}*704, {2,88,2}*704
   4-fold quotients : {2,44,2}*352, {4,22,2}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {4,8,2}*128a
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {4,4,2}*64, {2,8,2}*64
   44-fold quotients : {2,4,2}*32, {4,2,2}*32
   88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope