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Polytope of Type {22,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6,3}*1056
Also Known As : {{22,6|2},{6,3}4}. if this polytope has another name.
Group : SmallGroup(1056,1015)
Rank : 4
Schlafli Type : {22,6,3}
Number of vertices, edges, etc : 22, 88, 12, 4
Order of s0s1s2s3 : 44
Order of s0s1s2s3s2s1 : 2
Special Properties :
   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) :
   11-fold quotients : {2,6,3}*96
   22-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5, 41)(  6, 42)(  7, 43)(  8, 44)(  9, 37)( 10, 38)( 11, 39)( 12, 40)
( 13, 33)( 14, 34)( 15, 35)( 16, 36)( 17, 29)( 18, 30)( 19, 31)( 20, 32)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 49, 85)( 50, 86)( 51, 87)( 52, 88)
( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 77)( 58, 78)( 59, 79)( 60, 80)
( 61, 73)( 62, 74)( 63, 75)( 64, 76)( 65, 69)( 66, 70)( 67, 71)( 68, 72)
( 93,129)( 94,130)( 95,131)( 96,132)( 97,125)( 98,126)( 99,127)(100,128)
(101,121)(102,122)(103,123)(104,124)(105,117)(106,118)(107,119)(108,120)
(109,113)(110,114)(111,115)(112,116)(137,173)(138,174)(139,175)(140,176)
(141,169)(142,170)(143,171)(144,172)(145,165)(146,166)(147,167)(148,168)
(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)(156,160)
(181,217)(182,218)(183,219)(184,220)(185,213)(186,214)(187,215)(188,216)
(189,209)(190,210)(191,211)(192,212)(193,205)(194,206)(195,207)(196,208)
(197,201)(198,202)(199,203)(200,204)(225,261)(226,262)(227,263)(228,264)
(229,257)(230,258)(231,259)(232,260)(233,253)(234,254)(235,255)(236,256)
(237,249)(238,250)(239,251)(240,252)(241,245)(242,246)(243,247)(244,248);;
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);;
s3 := (  1,134)(  2,133)(  3,135)(  4,136)(  5,138)(  6,137)(  7,139)(  8,140)
(  9,142)( 10,141)( 11,143)( 12,144)( 13,146)( 14,145)( 15,147)( 16,148)
( 17,150)( 18,149)( 19,151)( 20,152)( 21,154)( 22,153)( 23,155)( 24,156)
( 25,158)( 26,157)( 27,159)( 28,160)( 29,162)( 30,161)( 31,163)( 32,164)
( 33,166)( 34,165)( 35,167)( 36,168)( 37,170)( 38,169)( 39,171)( 40,172)
( 41,174)( 42,173)( 43,175)( 44,176)( 45,222)( 46,221)( 47,223)( 48,224)
( 49,226)( 50,225)( 51,227)( 52,228)( 53,230)( 54,229)( 55,231)( 56,232)
( 57,234)( 58,233)( 59,235)( 60,236)( 61,238)( 62,237)( 63,239)( 64,240)
( 65,242)( 66,241)( 67,243)( 68,244)( 69,246)( 70,245)( 71,247)( 72,248)
( 73,250)( 74,249)( 75,251)( 76,252)( 77,254)( 78,253)( 79,255)( 80,256)
( 81,258)( 82,257)( 83,259)( 84,260)( 85,262)( 86,261)( 87,263)( 88,264)
( 89,178)( 90,177)( 91,179)( 92,180)( 93,182)( 94,181)( 95,183)( 96,184)
( 97,186)( 98,185)( 99,187)(100,188)(101,190)(102,189)(103,191)(104,192)
(105,194)(106,193)(107,195)(108,196)(109,198)(110,197)(111,199)(112,200)
(113,202)(114,201)(115,203)(116,204)(117,206)(118,205)(119,207)(120,208)
(121,210)(122,209)(123,211)(124,212)(125,214)(126,213)(127,215)(128,216)
(129,218)(130,217)(131,219)(132,220);;
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*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(264)!(  5, 41)(  6, 42)(  7, 43)(  8, 44)(  9, 37)( 10, 38)( 11, 39)
( 12, 40)( 13, 33)( 14, 34)( 15, 35)( 16, 36)( 17, 29)( 18, 30)( 19, 31)
( 20, 32)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 49, 85)( 50, 86)( 51, 87)
( 52, 88)( 53, 81)( 54, 82)( 55, 83)( 56, 84)( 57, 77)( 58, 78)( 59, 79)
( 60, 80)( 61, 73)( 62, 74)( 63, 75)( 64, 76)( 65, 69)( 66, 70)( 67, 71)
( 68, 72)( 93,129)( 94,130)( 95,131)( 96,132)( 97,125)( 98,126)( 99,127)
(100,128)(101,121)(102,122)(103,123)(104,124)(105,117)(106,118)(107,119)
(108,120)(109,113)(110,114)(111,115)(112,116)(137,173)(138,174)(139,175)
(140,176)(141,169)(142,170)(143,171)(144,172)(145,165)(146,166)(147,167)
(148,168)(149,161)(150,162)(151,163)(152,164)(153,157)(154,158)(155,159)
(156,160)(181,217)(182,218)(183,219)(184,220)(185,213)(186,214)(187,215)
(188,216)(189,209)(190,210)(191,211)(192,212)(193,205)(194,206)(195,207)
(196,208)(197,201)(198,202)(199,203)(200,204)(225,261)(226,262)(227,263)
(228,264)(229,257)(230,258)(231,259)(232,260)(233,253)(234,254)(235,255)
(236,256)(237,249)(238,250)(239,251)(240,252)(241,245)(242,246)(243,247)
(244,248);
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);
s3 := Sym(264)!(  1,134)(  2,133)(  3,135)(  4,136)(  5,138)(  6,137)(  7,139)
(  8,140)(  9,142)( 10,141)( 11,143)( 12,144)( 13,146)( 14,145)( 15,147)
( 16,148)( 17,150)( 18,149)( 19,151)( 20,152)( 21,154)( 22,153)( 23,155)
( 24,156)( 25,158)( 26,157)( 27,159)( 28,160)( 29,162)( 30,161)( 31,163)
( 32,164)( 33,166)( 34,165)( 35,167)( 36,168)( 37,170)( 38,169)( 39,171)
( 40,172)( 41,174)( 42,173)( 43,175)( 44,176)( 45,222)( 46,221)( 47,223)
( 48,224)( 49,226)( 50,225)( 51,227)( 52,228)( 53,230)( 54,229)( 55,231)
( 56,232)( 57,234)( 58,233)( 59,235)( 60,236)( 61,238)( 62,237)( 63,239)
( 64,240)( 65,242)( 66,241)( 67,243)( 68,244)( 69,246)( 70,245)( 71,247)
( 72,248)( 73,250)( 74,249)( 75,251)( 76,252)( 77,254)( 78,253)( 79,255)
( 80,256)( 81,258)( 82,257)( 83,259)( 84,260)( 85,262)( 86,261)( 87,263)
( 88,264)( 89,178)( 90,177)( 91,179)( 92,180)( 93,182)( 94,181)( 95,183)
( 96,184)( 97,186)( 98,185)( 99,187)(100,188)(101,190)(102,189)(103,191)
(104,192)(105,194)(106,193)(107,195)(108,196)(109,198)(110,197)(111,199)
(112,200)(113,202)(114,201)(115,203)(116,204)(117,206)(118,205)(119,207)
(120,208)(121,210)(122,209)(123,211)(124,212)(125,214)(126,213)(127,215)
(128,216)(129,218)(130,217)(131,219)(132,220);
poly := sub<Sym(264)|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*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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.
to this polytope