Polytope of Type {44,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,6}*1056
if this polytope has a name.
Group : SmallGroup(1056,1015)
Rank : 3
Schlafli Type : {44,6}
Number of vertices, edges, etc : 88, 264, 12
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {44,6}*528b
   4-fold quotients : {22,6}*264
   11-fold quotients : {4,6}*96
   12-fold quotients : {22,2}*88
   22-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   24-fold quotients : {11,2}*44
   44-fold quotients : {4,3}*24, {2,6}*24
   88-fold quotients : {2,3}*12
   132-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5, 43)(  6, 44)(  7, 41)(  8, 42)(  9, 39)( 10, 40)
( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 33)( 16, 34)( 17, 31)( 18, 32)
( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 25)( 24, 26)( 45, 47)( 46, 48)
( 49, 87)( 50, 88)( 51, 85)( 52, 86)( 53, 83)( 54, 84)( 55, 81)( 56, 82)
( 57, 79)( 58, 80)( 59, 77)( 60, 78)( 61, 75)( 62, 76)( 63, 73)( 64, 74)
( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 89, 91)( 90, 92)( 93,131)( 94,132)
( 95,129)( 96,130)( 97,127)( 98,128)( 99,125)(100,126)(101,123)(102,124)
(103,121)(104,122)(105,119)(106,120)(107,117)(108,118)(109,115)(110,116)
(111,113)(112,114)(133,135)(134,136)(137,175)(138,176)(139,173)(140,174)
(141,171)(142,172)(143,169)(144,170)(145,167)(146,168)(147,165)(148,166)
(149,163)(150,164)(151,161)(152,162)(153,159)(154,160)(155,157)(156,158)
(177,179)(178,180)(181,219)(182,220)(183,217)(184,218)(185,215)(186,216)
(187,213)(188,214)(189,211)(190,212)(191,209)(192,210)(193,207)(194,208)
(195,205)(196,206)(197,203)(198,204)(199,201)(200,202)(221,223)(222,224)
(225,263)(226,264)(227,261)(228,262)(229,259)(230,260)(231,257)(232,258)
(233,255)(234,256)(235,253)(236,254)(237,251)(238,252)(239,249)(240,250)
(241,247)(242,248)(243,245)(244,246);;
s1 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 41)( 10, 42)( 11, 44)( 12, 43)
( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)( 20, 35)
( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 27, 28)( 45, 93)( 46, 94)( 47, 96)
( 48, 95)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53,129)( 54,130)( 55,132)
( 56,131)( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)( 63,124)
( 64,123)( 65,117)( 66,118)( 67,120)( 68,119)( 69,113)( 70,114)( 71,116)
( 72,115)( 73,109)( 74,110)( 75,112)( 76,111)( 77,105)( 78,106)( 79,108)
( 80,107)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)( 87,100)
( 88, 99)(133,137)(134,138)(135,140)(136,139)(141,173)(142,174)(143,176)
(144,175)(145,169)(146,170)(147,172)(148,171)(149,165)(150,166)(151,168)
(152,167)(153,161)(154,162)(155,164)(156,163)(159,160)(177,225)(178,226)
(179,228)(180,227)(181,221)(182,222)(183,224)(184,223)(185,261)(186,262)
(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,253)(194,254)
(195,256)(196,255)(197,249)(198,250)(199,252)(200,251)(201,245)(202,246)
(203,248)(204,247)(205,241)(206,242)(207,244)(208,243)(209,237)(210,238)
(211,240)(212,239)(213,233)(214,234)(215,236)(216,235)(217,229)(218,230)
(219,232)(220,231);;
s2 := (  1,177)(  2,180)(  3,179)(  4,178)(  5,181)(  6,184)(  7,183)(  8,182)
(  9,185)( 10,188)( 11,187)( 12,186)( 13,189)( 14,192)( 15,191)( 16,190)
( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)( 24,198)
( 25,201)( 26,204)( 27,203)( 28,202)( 29,205)( 30,208)( 31,207)( 32,206)
( 33,209)( 34,212)( 35,211)( 36,210)( 37,213)( 38,216)( 39,215)( 40,214)
( 41,217)( 42,220)( 43,219)( 44,218)( 45,133)( 46,136)( 47,135)( 48,134)
( 49,137)( 50,140)( 51,139)( 52,138)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)( 64,150)
( 65,153)( 66,156)( 67,155)( 68,154)( 69,157)( 70,160)( 71,159)( 72,158)
( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)( 80,166)
( 81,169)( 82,172)( 83,171)( 84,170)( 85,173)( 86,176)( 87,175)( 88,174)
( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)( 96,226)
( 97,229)( 98,232)( 99,231)(100,230)(101,233)(102,236)(103,235)(104,234)
(105,237)(106,240)(107,239)(108,238)(109,241)(110,244)(111,243)(112,242)
(113,245)(114,248)(115,247)(116,246)(117,249)(118,252)(119,251)(120,250)
(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)(128,258)
(129,261)(130,264)(131,263)(132,262);;
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*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*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(264)!(  1,  3)(  2,  4)(  5, 43)(  6, 44)(  7, 41)(  8, 42)(  9, 39)
( 10, 40)( 11, 37)( 12, 38)( 13, 35)( 14, 36)( 15, 33)( 16, 34)( 17, 31)
( 18, 32)( 19, 29)( 20, 30)( 21, 27)( 22, 28)( 23, 25)( 24, 26)( 45, 47)
( 46, 48)( 49, 87)( 50, 88)( 51, 85)( 52, 86)( 53, 83)( 54, 84)( 55, 81)
( 56, 82)( 57, 79)( 58, 80)( 59, 77)( 60, 78)( 61, 75)( 62, 76)( 63, 73)
( 64, 74)( 65, 71)( 66, 72)( 67, 69)( 68, 70)( 89, 91)( 90, 92)( 93,131)
( 94,132)( 95,129)( 96,130)( 97,127)( 98,128)( 99,125)(100,126)(101,123)
(102,124)(103,121)(104,122)(105,119)(106,120)(107,117)(108,118)(109,115)
(110,116)(111,113)(112,114)(133,135)(134,136)(137,175)(138,176)(139,173)
(140,174)(141,171)(142,172)(143,169)(144,170)(145,167)(146,168)(147,165)
(148,166)(149,163)(150,164)(151,161)(152,162)(153,159)(154,160)(155,157)
(156,158)(177,179)(178,180)(181,219)(182,220)(183,217)(184,218)(185,215)
(186,216)(187,213)(188,214)(189,211)(190,212)(191,209)(192,210)(193,207)
(194,208)(195,205)(196,206)(197,203)(198,204)(199,201)(200,202)(221,223)
(222,224)(225,263)(226,264)(227,261)(228,262)(229,259)(230,260)(231,257)
(232,258)(233,255)(234,256)(235,253)(236,254)(237,251)(238,252)(239,249)
(240,250)(241,247)(242,248)(243,245)(244,246);
s1 := Sym(264)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 41)( 10, 42)( 11, 44)
( 12, 43)( 13, 37)( 14, 38)( 15, 40)( 16, 39)( 17, 33)( 18, 34)( 19, 36)
( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 27, 28)( 45, 93)( 46, 94)
( 47, 96)( 48, 95)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53,129)( 54,130)
( 55,132)( 56,131)( 57,125)( 58,126)( 59,128)( 60,127)( 61,121)( 62,122)
( 63,124)( 64,123)( 65,117)( 66,118)( 67,120)( 68,119)( 69,113)( 70,114)
( 71,116)( 72,115)( 73,109)( 74,110)( 75,112)( 76,111)( 77,105)( 78,106)
( 79,108)( 80,107)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)
( 87,100)( 88, 99)(133,137)(134,138)(135,140)(136,139)(141,173)(142,174)
(143,176)(144,175)(145,169)(146,170)(147,172)(148,171)(149,165)(150,166)
(151,168)(152,167)(153,161)(154,162)(155,164)(156,163)(159,160)(177,225)
(178,226)(179,228)(180,227)(181,221)(182,222)(183,224)(184,223)(185,261)
(186,262)(187,264)(188,263)(189,257)(190,258)(191,260)(192,259)(193,253)
(194,254)(195,256)(196,255)(197,249)(198,250)(199,252)(200,251)(201,245)
(202,246)(203,248)(204,247)(205,241)(206,242)(207,244)(208,243)(209,237)
(210,238)(211,240)(212,239)(213,233)(214,234)(215,236)(216,235)(217,229)
(218,230)(219,232)(220,231);
s2 := Sym(264)!(  1,177)(  2,180)(  3,179)(  4,178)(  5,181)(  6,184)(  7,183)
(  8,182)(  9,185)( 10,188)( 11,187)( 12,186)( 13,189)( 14,192)( 15,191)
( 16,190)( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)
( 24,198)( 25,201)( 26,204)( 27,203)( 28,202)( 29,205)( 30,208)( 31,207)
( 32,206)( 33,209)( 34,212)( 35,211)( 36,210)( 37,213)( 38,216)( 39,215)
( 40,214)( 41,217)( 42,220)( 43,219)( 44,218)( 45,133)( 46,136)( 47,135)
( 48,134)( 49,137)( 50,140)( 51,139)( 52,138)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,145)( 58,148)( 59,147)( 60,146)( 61,149)( 62,152)( 63,151)
( 64,150)( 65,153)( 66,156)( 67,155)( 68,154)( 69,157)( 70,160)( 71,159)
( 72,158)( 73,161)( 74,164)( 75,163)( 76,162)( 77,165)( 78,168)( 79,167)
( 80,166)( 81,169)( 82,172)( 83,171)( 84,170)( 85,173)( 86,176)( 87,175)
( 88,174)( 89,221)( 90,224)( 91,223)( 92,222)( 93,225)( 94,228)( 95,227)
( 96,226)( 97,229)( 98,232)( 99,231)(100,230)(101,233)(102,236)(103,235)
(104,234)(105,237)(106,240)(107,239)(108,238)(109,241)(110,244)(111,243)
(112,242)(113,245)(114,248)(115,247)(116,246)(117,249)(118,252)(119,251)
(120,250)(121,253)(122,256)(123,255)(124,254)(125,257)(126,260)(127,259)
(128,258)(129,261)(130,264)(131,263)(132,262);
poly := sub<Sym(264)|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*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*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