Polytope of Type {22,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,4,3}*1056
Also Known As : {{22,4|2},{4,3}}. if this polytope has another name.
Group : SmallGroup(1056,1015)
Rank : 4
Schlafli Type : {22,4,3}
Number of vertices, edges, etc : 22, 88, 12, 6
Order of s0s1s2s3 : 66
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) :
4-fold quotients : {22,2,3}*264
8-fold quotients : {11,2,3}*132
11-fold quotients : {2,4,3}*96
22-fold quotients : {2,4,3}*48
44-fold quotients : {2,2,3}*24
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 := ( 1,139)( 2,140)( 3,137)( 4,138)( 5,135)( 6,136)( 7,133)( 8,134)
( 9,175)( 10,176)( 11,173)( 12,174)( 13,171)( 14,172)( 15,169)( 16,170)
( 17,167)( 18,168)( 19,165)( 20,166)( 21,163)( 22,164)( 23,161)( 24,162)
( 25,159)( 26,160)( 27,157)( 28,158)( 29,155)( 30,156)( 31,153)( 32,154)
( 33,151)( 34,152)( 35,149)( 36,150)( 37,147)( 38,148)( 39,145)( 40,146)
( 41,143)( 42,144)( 43,141)( 44,142)( 45,183)( 46,184)( 47,181)( 48,182)
( 49,179)( 50,180)( 51,177)( 52,178)( 53,219)( 54,220)( 55,217)( 56,218)
( 57,215)( 58,216)( 59,213)( 60,214)( 61,211)( 62,212)( 63,209)( 64,210)
( 65,207)( 66,208)( 67,205)( 68,206)( 69,203)( 70,204)( 71,201)( 72,202)
( 73,199)( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)
( 81,191)( 82,192)( 83,189)( 84,190)( 85,187)( 86,188)( 87,185)( 88,186)
( 89,227)( 90,228)( 91,225)( 92,226)( 93,223)( 94,224)( 95,221)( 96,222)
( 97,263)( 98,264)( 99,261)(100,262)(101,259)(102,260)(103,257)(104,258)
(105,255)(106,256)(107,253)(108,254)(109,251)(110,252)(111,249)(112,250)
(113,247)(114,248)(115,245)(116,246)(117,243)(118,244)(119,241)(120,242)
(121,239)(122,240)(123,237)(124,238)(125,235)(126,236)(127,233)(128,234)
(129,231)(130,232)(131,229)(132,230);;
s2 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)( 31, 32)
( 35, 36)( 39, 40)( 43, 44)( 45, 89)( 46, 90)( 47, 92)( 48, 91)( 49, 93)
( 50, 94)( 51, 96)( 52, 95)( 53, 97)( 54, 98)( 55,100)( 56, 99)( 57,101)
( 58,102)( 59,104)( 60,103)( 61,105)( 62,106)( 63,108)( 64,107)( 65,109)
( 66,110)( 67,112)( 68,111)( 69,113)( 70,114)( 71,116)( 72,115)( 73,117)
( 74,118)( 75,120)( 76,119)( 77,121)( 78,122)( 79,124)( 80,123)( 81,125)
( 82,126)( 83,128)( 84,127)( 85,129)( 86,130)( 87,132)( 88,131)(135,136)
(139,140)(143,144)(147,148)(151,152)(155,156)(159,160)(163,164)(167,168)
(171,172)(175,176)(177,221)(178,222)(179,224)(180,223)(181,225)(182,226)
(183,228)(184,227)(185,229)(186,230)(187,232)(188,231)(189,233)(190,234)
(191,236)(192,235)(193,237)(194,238)(195,240)(196,239)(197,241)(198,242)
(199,244)(200,243)(201,245)(202,246)(203,248)(204,247)(205,249)(206,250)
(207,252)(208,251)(209,253)(210,254)(211,256)(212,255)(213,257)(214,258)
(215,260)(216,259)(217,261)(218,262)(219,264)(220,263);;
s3 := ( 1, 45)( 2, 48)( 3, 47)( 4, 46)( 5, 49)( 6, 52)( 7, 51)( 8, 50)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 57)( 14, 60)( 15, 59)( 16, 58)
( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)( 24, 66)
( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 73)( 30, 76)( 31, 75)( 32, 74)
( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 81)( 38, 84)( 39, 83)( 40, 82)
( 41, 85)( 42, 88)( 43, 87)( 44, 86)( 90, 92)( 94, 96)( 98,100)(102,104)
(106,108)(110,112)(114,116)(118,120)(122,124)(126,128)(130,132)(133,177)
(134,180)(135,179)(136,178)(137,181)(138,184)(139,183)(140,182)(141,185)
(142,188)(143,187)(144,186)(145,189)(146,192)(147,191)(148,190)(149,193)
(150,196)(151,195)(152,194)(153,197)(154,200)(155,199)(156,198)(157,201)
(158,204)(159,203)(160,202)(161,205)(162,208)(163,207)(164,206)(165,209)
(166,212)(167,211)(168,210)(169,213)(170,216)(171,215)(172,214)(173,217)
(174,220)(175,219)(176,218)(222,224)(226,228)(230,232)(234,236)(238,240)
(242,244)(246,248)(250,252)(254,256)(258,260)(262,264);;
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*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)!( 1,139)( 2,140)( 3,137)( 4,138)( 5,135)( 6,136)( 7,133)
( 8,134)( 9,175)( 10,176)( 11,173)( 12,174)( 13,171)( 14,172)( 15,169)
( 16,170)( 17,167)( 18,168)( 19,165)( 20,166)( 21,163)( 22,164)( 23,161)
( 24,162)( 25,159)( 26,160)( 27,157)( 28,158)( 29,155)( 30,156)( 31,153)
( 32,154)( 33,151)( 34,152)( 35,149)( 36,150)( 37,147)( 38,148)( 39,145)
( 40,146)( 41,143)( 42,144)( 43,141)( 44,142)( 45,183)( 46,184)( 47,181)
( 48,182)( 49,179)( 50,180)( 51,177)( 52,178)( 53,219)( 54,220)( 55,217)
( 56,218)( 57,215)( 58,216)( 59,213)( 60,214)( 61,211)( 62,212)( 63,209)
( 64,210)( 65,207)( 66,208)( 67,205)( 68,206)( 69,203)( 70,204)( 71,201)
( 72,202)( 73,199)( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)
( 80,194)( 81,191)( 82,192)( 83,189)( 84,190)( 85,187)( 86,188)( 87,185)
( 88,186)( 89,227)( 90,228)( 91,225)( 92,226)( 93,223)( 94,224)( 95,221)
( 96,222)( 97,263)( 98,264)( 99,261)(100,262)(101,259)(102,260)(103,257)
(104,258)(105,255)(106,256)(107,253)(108,254)(109,251)(110,252)(111,249)
(112,250)(113,247)(114,248)(115,245)(116,246)(117,243)(118,244)(119,241)
(120,242)(121,239)(122,240)(123,237)(124,238)(125,235)(126,236)(127,233)
(128,234)(129,231)(130,232)(131,229)(132,230);
s2 := Sym(264)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 23, 24)( 27, 28)
( 31, 32)( 35, 36)( 39, 40)( 43, 44)( 45, 89)( 46, 90)( 47, 92)( 48, 91)
( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 97)( 54, 98)( 55,100)( 56, 99)
( 57,101)( 58,102)( 59,104)( 60,103)( 61,105)( 62,106)( 63,108)( 64,107)
( 65,109)( 66,110)( 67,112)( 68,111)( 69,113)( 70,114)( 71,116)( 72,115)
( 73,117)( 74,118)( 75,120)( 76,119)( 77,121)( 78,122)( 79,124)( 80,123)
( 81,125)( 82,126)( 83,128)( 84,127)( 85,129)( 86,130)( 87,132)( 88,131)
(135,136)(139,140)(143,144)(147,148)(151,152)(155,156)(159,160)(163,164)
(167,168)(171,172)(175,176)(177,221)(178,222)(179,224)(180,223)(181,225)
(182,226)(183,228)(184,227)(185,229)(186,230)(187,232)(188,231)(189,233)
(190,234)(191,236)(192,235)(193,237)(194,238)(195,240)(196,239)(197,241)
(198,242)(199,244)(200,243)(201,245)(202,246)(203,248)(204,247)(205,249)
(206,250)(207,252)(208,251)(209,253)(210,254)(211,256)(212,255)(213,257)
(214,258)(215,260)(216,259)(217,261)(218,262)(219,264)(220,263);
s3 := Sym(264)!( 1, 45)( 2, 48)( 3, 47)( 4, 46)( 5, 49)( 6, 52)( 7, 51)
( 8, 50)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 57)( 14, 60)( 15, 59)
( 16, 58)( 17, 61)( 18, 64)( 19, 63)( 20, 62)( 21, 65)( 22, 68)( 23, 67)
( 24, 66)( 25, 69)( 26, 72)( 27, 71)( 28, 70)( 29, 73)( 30, 76)( 31, 75)
( 32, 74)( 33, 77)( 34, 80)( 35, 79)( 36, 78)( 37, 81)( 38, 84)( 39, 83)
( 40, 82)( 41, 85)( 42, 88)( 43, 87)( 44, 86)( 90, 92)( 94, 96)( 98,100)
(102,104)(106,108)(110,112)(114,116)(118,120)(122,124)(126,128)(130,132)
(133,177)(134,180)(135,179)(136,178)(137,181)(138,184)(139,183)(140,182)
(141,185)(142,188)(143,187)(144,186)(145,189)(146,192)(147,191)(148,190)
(149,193)(150,196)(151,195)(152,194)(153,197)(154,200)(155,199)(156,198)
(157,201)(158,204)(159,203)(160,202)(161,205)(162,208)(163,207)(164,206)
(165,209)(166,212)(167,211)(168,210)(169,213)(170,216)(171,215)(172,214)
(173,217)(174,220)(175,219)(176,218)(222,224)(226,228)(230,232)(234,236)
(238,240)(242,244)(246,248)(250,252)(254,256)(258,260)(262,264);
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*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