Polytope of Type {88,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,4,2}*1408b
if this polytope has a name.
Group : SmallGroup(1408,13836)
Rank : 4
Schlafli Type : {88,4,2}
Number of vertices, edges, etc : 88, 176, 4, 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 : {44,4,2}*704
   4-fold quotients : {44,2,2}*352, {22,4,2}*352
   8-fold quotients : {22,2,2}*176
   11-fold quotients : {8,4,2}*128b
   16-fold quotients : {11,2,2}*88
   22-fold quotients : {4,4,2}*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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)
( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)
( 82, 85)( 83, 84)( 89,133)( 90,143)( 91,142)( 92,141)( 93,140)( 94,139)
( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,144)(101,154)(102,153)
(103,152)(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)(110,145)
(111,166)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,170)
(119,169)(120,168)(121,167)(122,155)(123,165)(124,164)(125,163)(126,162)
(127,161)(128,160)(129,159)(130,158)(131,157)(132,156);;
s1 := (  1, 90)(  2, 89)(  3, 99)(  4, 98)(  5, 97)(  6, 96)(  7, 95)(  8, 94)
(  9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)( 24,111)
( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)( 32,114)
( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)( 40,128)
( 41,127)( 42,126)( 43,125)( 44,124)( 45,145)( 46,144)( 47,154)( 48,153)
( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,146)( 56,134)
( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)( 64,137)
( 65,136)( 66,135)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,156)( 79,155)( 80,165)
( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)( 87,158)( 88,157);;
s2 := ( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)( 52, 63)
( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)
( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 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)(133,166)(134,167)(135,168)(136,169)
(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)(144,155)
(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)(152,163)
(153,164)(154,165);;
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, 
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*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*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(178)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)
( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 45, 56)( 46, 66)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)
( 55, 57)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)
( 81, 86)( 82, 85)( 83, 84)( 89,133)( 90,143)( 91,142)( 92,141)( 93,140)
( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,144)(101,154)
(102,153)(103,152)(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)
(110,145)(111,166)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)
(118,170)(119,169)(120,168)(121,167)(122,155)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,157)(132,156);
s1 := Sym(178)!(  1, 90)(  2, 89)(  3, 99)(  4, 98)(  5, 97)(  6, 96)(  7, 95)
(  8, 94)(  9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,112)
( 24,111)( 25,121)( 26,120)( 27,119)( 28,118)( 29,117)( 30,116)( 31,115)
( 32,114)( 33,113)( 34,123)( 35,122)( 36,132)( 37,131)( 38,130)( 39,129)
( 40,128)( 41,127)( 42,126)( 43,125)( 44,124)( 45,145)( 46,144)( 47,154)
( 48,153)( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,146)
( 56,134)( 57,133)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,136)( 66,135)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)
( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,156)( 79,155)
( 80,165)( 81,164)( 82,163)( 83,162)( 84,161)( 85,160)( 86,159)( 87,158)
( 88,157);
s2 := Sym(178)!( 45, 56)( 46, 57)( 47, 58)( 48, 59)( 49, 60)( 50, 61)( 51, 62)
( 52, 63)( 53, 64)( 54, 65)( 55, 66)( 67, 78)( 68, 79)( 69, 80)( 70, 81)
( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)( 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)(133,166)(134,167)(135,168)
(136,169)(137,170)(138,171)(139,172)(140,173)(141,174)(142,175)(143,176)
(144,155)(145,156)(146,157)(147,158)(148,159)(149,160)(150,161)(151,162)
(152,163)(153,164)(154,165);
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, 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*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope