Polytope of Type {88,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,4}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6495)
Rank : 3
Schlafli Type : {88,4}
Number of vertices, edges, etc : 176, 352, 8
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {44,4}*704
   4-fold quotients : {44,4}*352
   8-fold quotients : {44,2}*176, {22,4}*176
   11-fold quotients : {8,4}*128b
   16-fold quotients : {22,2}*88
   22-fold quotients : {4,4}*64
   32-fold quotients : {11,2}*44
   44-fold quotients : {4,4}*32
   88-fold quotients : {2,4}*16, {4,2}*16
   176-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*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*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 >;

References : None.
to this polytope