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Polytope of Type {44,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,8}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6496)
Rank : 3
Schlafli Type : {44,8}
Number of vertices, edges, etc : 88, 352, 16
Order of s0s1s2 : 44
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
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 : {4,8}*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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 78)( 46, 88)( 47, 87)( 48, 86)
( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)( 56, 67)
( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)( 63, 71)( 64, 70)
( 65, 69)( 66, 68)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)
(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)
(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(133,166)(134,176)
(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)(142,168)
(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)
(151,159)(152,158)(153,157)(154,156);;
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 := (  1, 89)(  2, 90)(  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 95)(  8, 96)
(  9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)
( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)
( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)
( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)
( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)( 48,169)
( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,155)
( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)( 64,163)
( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)
( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)
( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143);;
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, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(176)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 78)( 46, 88)( 47, 87)
( 48, 86)( 49, 85)( 50, 84)( 51, 83)( 52, 82)( 53, 81)( 54, 80)( 55, 79)
( 56, 67)( 57, 77)( 58, 76)( 59, 75)( 60, 74)( 61, 73)( 62, 72)( 63, 71)
( 64, 70)( 65, 69)( 66, 68)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)
(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)
(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(133,166)
(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)
(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)(149,161)
(150,160)(151,159)(152,158)(153,157)(154,156);
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)!(  1, 89)(  2, 90)(  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 95)
(  8, 96)(  9, 97)( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)
( 16,104)( 17,105)( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)
( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)
( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)
( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)
( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)
( 56,155)( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)
( 64,163)( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)
( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)
( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)
( 88,143);
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, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*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 >; 
 
References : None.
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