Polytope of Type {2,88,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,88,4}*1408a
if this polytope has a name.
Group : SmallGroup(1408,13688)
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, {2,88,2}*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}*128a
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {2,4,4}*64, {2,8,2}*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)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)( 49, 67)( 50, 66)
( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 69, 80)
( 70, 90)( 71, 89)( 72, 88)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)
( 78, 82)( 79, 81)( 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)
(113,157)(114,167)(115,166)(116,165)(117,164)(118,163)(119,162)(120,161)
(121,160)(122,159)(123,158)(124,168)(125,178)(126,177)(127,176)(128,175)
(129,174)(130,173)(131,172)(132,171)(133,170)(134,169);;
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 := ( 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);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 47, 58)( 48, 68)( 49, 67)
( 50, 66)( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)
( 69, 80)( 70, 90)( 71, 89)( 72, 88)( 73, 87)( 74, 86)( 75, 85)( 76, 84)
( 77, 83)( 78, 82)( 79, 81)( 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)(113,157)(114,167)(115,166)(116,165)(117,164)(118,163)(119,162)
(120,161)(121,160)(122,159)(123,158)(124,168)(125,178)(126,177)(127,176)
(128,175)(129,174)(130,173)(131,172)(132,171)(133,170)(134,169);
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)!( 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);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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